From 6f926ee4aec7f2f49e26dd7d36a1a2925d22ec8d Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 10:31:31 +0300 Subject: [PATCH 01/23] First draft of paper --- .github/workflows/draft-pdf.yaml | 23 +++++ joss/paper.bib | 74 ++++++++++++++ joss/paper.md | 159 +++++++++++++++++++++++++++++++ 3 files changed, 256 insertions(+) create mode 100644 .github/workflows/draft-pdf.yaml create mode 100644 joss/paper.bib create mode 100644 joss/paper.md diff --git a/.github/workflows/draft-pdf.yaml b/.github/workflows/draft-pdf.yaml new file mode 100644 index 0000000..f24d0d0 --- /dev/null +++ b/.github/workflows/draft-pdf.yaml @@ -0,0 +1,23 @@ +on: [push] + +jobs: + paper: + runs-on: ubuntu-latest + name: Paper Draft + steps: + - name: Checkout + uses: actions/checkout@v4 + - name: Build draft PDF + uses: openjournals/openjournals-draft-action@master + with: + journal: joss + # This should be the path to the paper within your repo. + paper-path: joss/paper.md + - name: Upload + uses: actions/upload-artifact@v1 + with: + name: paper + # This is the output path where Pandoc will write the compiled + # PDF. Note, this should be the same directory as the input + # paper.md + path: joss/paper.pdf \ No newline at end of file diff --git a/joss/paper.bib b/joss/paper.bib new file mode 100644 index 0000000..f4c30d4 --- /dev/null +++ b/joss/paper.bib @@ -0,0 +1,74 @@ +@article{Ravasi:2020, + author = {M. Ravasi and I. Vasconcelos}, + title = "{PyLops - A linear-operator Python library for scalable algebra and optimization}", + journal = {SoftwareX}, + year = 2020, + volume = 11, + doi = {10.1016/j.softx.2019.100361}, + url = {https://www.sciencedirect.com/science/article/pii/S2352711019301086} +} + + +----- + + + +@article{Pearson:2017, + url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P}, + Archiveprefix = {arXiv}, + Author = {{Pearson}, S. and {Price-Whelan}, A.~M. and {Johnston}, K.~V.}, + Eprint = {1703.04627}, + Journal = {ArXiv e-prints}, + Keywords = {Astrophysics - Astrophysics of Galaxies}, + Month = mar, + Title = {{Gaps in Globular Cluster Streams: Pal 5 and the Galactic Bar}}, + Year = 2017 +} + +@book{Binney:2008, + url = {http://adsabs.harvard.edu/abs/2008gady.book.....B}, + Author = {{Binney}, J. and {Tremaine}, S.}, + Booktitle = {Galactic Dynamics: Second Edition, by James Binney and Scott Tremaine.~ISBN 978-0-691-13026-2 (HB).~Published by Princeton University Press, Princeton, NJ USA, 2008.}, + Publisher = {Princeton University Press}, + Title = {{Galactic Dynamics: Second Edition}}, + Year = 2008 +} + +@article{gaia, + author = {{Gaia Collaboration}}, + title = "{The Gaia mission}", + journal = {Astronomy and Astrophysics}, + archivePrefix = "arXiv", + eprint = {1609.04153}, + primaryClass = "astro-ph.IM", + keywords = {space vehicles: instruments, Galaxy: structure, astrometry, parallaxes, proper motions, telescopes}, + year = 2016, + month = nov, + volume = 595, + doi = {10.1051/0004-6361/201629272}, + url = {http://adsabs.harvard.edu/abs/2016A%26A...595A...1G}, +} + +@article{astropy, + author = {{Astropy Collaboration}}, + title = "{Astropy: A community Python package for astronomy}", + journal = {Astronomy and Astrophysics}, + archivePrefix = "arXiv", + eprint = {1307.6212}, + primaryClass = "astro-ph.IM", + keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools}, + year = 2013, + month = oct, + volume = 558, + doi = {10.1051/0004-6361/201322068}, + url = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A} +} + +@misc{fidgit, + author = {A. M. Smith and K. Thaney and M. Hahnel}, + title = {Fidgit: An ungodly union of GitHub and Figshare}, + year = {2020}, + publisher = {GitHub}, + journal = {GitHub repository}, + url = {https://github.com/arfon/fidgit} +} \ No newline at end of file diff --git a/joss/paper.md b/joss/paper.md new file mode 100644 index 0000000..2655d72 --- /dev/null +++ b/joss/paper.md @@ -0,0 +1,159 @@ +--- +title: 'PyProximal - scalable convex optimization in Python' +tags: + - Python + - optimization + - proximal +authors: + - name: Matteo Ravasi + orcid: 0000-0003-0020-2721 + corresponding: true # (This is how to denote the corresponding author) + affiliation: "1" # (Multiple affiliations must be quoted) +affiliations: + - name: Earth Science and Engineering, Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia + index: 1 +date: 19 December 2023 +bibliography: paper.bib + + + +# Summary + +A broad class of problems in scientific disciplines ranging from image processing and astrophysics, +to geophysics and medical imaging call for the optimization of convex, non-smooth objective functions. +PyProximal is a Python-based library providing users with an extensive suite of state-of-the-art proximal +operators and algorithms. + +Whereas practitioners are usually very familiar with gradient-based optimization and the associated +first- or second-order iterative schemes commonly used to solve unconstrained, smooth optimization problems, proximal +algorithms can be viewed as analogous tools for non-smooth and possibly constrained versions of such problems. These +algorithms sit at a higher level of abstraction than classical algorithms like steepest descent or Newton’s method and +require a basic operation to be performed at each iteration: the evaluation of the so-called proximal operator of the +functional to be optimized. + +In summary, PyProximal aims to democratize the application of convex optimization to scientific problems, providing +users with all the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, +convex objective functions in a high-level, abstract fashion, shielding them away from any unneeded mathematical and +implementation details. + + +# Statement of need + +`PyProximal` is a NUMFOCUS-affiliated Python package for convex optimization developed as an integral part of the `PyLops` framework. +It provides practitioners in a variety of scientific disciplines with an easy-to-use Python based framework to +define and solve composite convex objective functions arising in many modern inverse problems. Its API was +designed to provide a class-based and user-friendly interface to proximal operators coupled with function-based +optimizers; because of its modular design, researchers in the field of convex optimization can also benefit from this +package when developing new algorithms in a number of ways: first, they can easily include their newly developed proximal operators +and solvers; second, they can compare these methods with state-of-the-art algorithms already provided in the package + +`PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], our main package for matrix-free linear algebra +and optimization. More specifically, some of `PyLops`'s linear operators and solvers used leveraged in the implementation +of proximal operators that require access to linear operators (e.g., numerical derivatives) and least-squares solvers +(e.g., conjugate gradient). Whilst other similar packages exist in the Python ecosystem, their design usually leads to a +tight coupling between linear operators and solvers and proximal operators and solvers. On the other hand, by following the +Separation of Concerns (SoC) design principle, we reduce to a minimum the overlap between the two libraries, easing both +their development and maintenance, as well as allowing newcomers to learn how to solve inverse problems in a step-by-step manner. +As such, `PyProximal` can be ultimately described as a light-weight extension of `PyLops` that users of the former can very easily +learn and use in short time and with minimal additional effort. + +`PyProximal` was designed to be used by both researchers and students in applied mathematics and engineering courses. +It has already been featured in a number of scientific publications [XX] and in a graduate-level course on inverse problems [XX]. +As the adoption of the library grows across many disciplies, we believe that `PyProximal` will enable exciting scientific discoveries +in a variety of scientific problems with societal impact. + + +# Mathematical framework + +Convex optimization is routinely used to solve problems of the form: + +\begin{equation} +\label{eq:problem} +min_\mathbf{x} f(\mathbf{x}) +g(\mathbf{Ax}) +\end{equation} + +where $f$ and $g$ are possibly non-smooth convex functionals and $\mathbf{A}$ is a linear operator. A special case, +appearing in many scientific applications, is represented by f=1/2 \Vert y - \mathbf{Gx}\Vert_2^2, which identifies +the so-called data misfit term. Here, $\mathbf{G}$ is the modeling operator representing the underlying physical +process the links the unknown model vector $\mathbf{x}$ to the vector of observations $\mathbf{d}$. In this case, +we usually refer to g as the regularization term, where one or multiple terms are added to the objective function to +promote certain features in the sought after solution and/or constraint it within a given set of allowed solutions. + +Independently from the algorithm used to optimize such a cost function, a common feature of all proximal algorithms is +represented by the fact that one must be able to repeatedly evaluate the proximal operator of f and/or g. The proximal +operator of a function f is defined as +… +Whilst evaluating a proximal operator does itself require solving an optimization problem, these subproblems often +admit closed form solutions or can be solved very quickly with ad-hoc specialized methods. Several of such proximal +operators are efficiently implemented in the PyProximal library. + +Finally, there exists three main families of proximal algorithms that can be used to solve various flavors of equation +\autoref{eq:problem} , namely: + +- Proximal gradient method: this method, also commonly referred to as the FBS algorithm red, is usually the + preferred choice when A=I (I.e. identity). Accelerated versions such as the FISTA and TWist algorithms exist + and are usually preferred to the vanilla FBS method; +- Alternating direction of multipliers: this method is based on the well-known splitting strategy and can be used + for a broader class of problem than FBS and its accelarated versions. … +- Primal-dual: another popular algorithm able to tackle the generic problem in equation 1 with any choice of A. + It reformulates the original problem into its primal-dual version of solves a saddle optimization problem. + +# Code structure + +# Pedagogic example + +Let's begin with a simple example showing how to compute the proximal operator of the L1 norm of a vector: + +import numpy as np +from pyproximal import L1 + +l1 = L1() +x = np.arange(-5, 5, 0.1) +xp = l1.prox(x, 1) + +As shown in line 4, one first initialized the operator. Subsequently, the prox method can be invoked to compute the proximal on a vector x with a given tau (here tau=1.). Note that this is a common pattern for all proximal operators in PyProximal + +Moving on, we can how see how such a proximal operator can be used to solve a basic denoising problem of the form: + + +# Research applications + +PyProximal has already been featured in a number of scientific publications: + +- Joint inversion and segmentation of subsurface models: when inverting geophysical data for subsurface priorities, + a prior information that we would like to include in the inversion process is represented by the presence of a + discrete number of rock units, which can be parametrized in terms of their expected mean (or most likely value). + Ravasi and Birnie (2022) framed such a problem as a joint inversion and segmentation where the underlying optimization + is solved in alternating fashion using the Primal-dual algorithm. +- Plug-and-Play (PnP) priors: introduced in 2013 by Vent, in the PnP framework any proximal operator is interpreted + as a denoising problem and solved by means of any statistical or deep learning based denoiser. Recently, Romero + +# Citations + +Citations to entries in paper.bib should be in +[rMarkdown](http://rmarkdown.rstudio.com/authoring_bibliographies_and_citations.html) +format. + +If you want to cite a software repository URL (e.g. something on GitHub without a preferred +citation) then you can do it with the example BibTeX entry below for @fidgit. + +For a quick reference, the following citation commands can be used: +- `@author:2001` -> "Author et al. (2001)" +- `[@author:2001]` -> "(Author et al., 2001)" +- `[@author1:2001; @author2:2001]` -> "(Author1 et al., 2001; Author2 et al., 2002)" + +# Figures + +Figures can be included like this: +![Caption for example figure.\label{fig:example}](figure.png) +and referenced from text using \autoref{fig:example}. + +Figure sizes can be customized by adding an optional second parameter: +![Caption for example figure.](figure.png){ width=20% } + +# Acknowledgements + +We acknowledge contributions from Brigitta Sipocz, Syrtis Major, and Semyeong +Oh, and support from Kathryn Johnston during the genesis of this project. + +# References \ No newline at end of file From 1453d328e16d9b6ea5dbd2ad9b17cf3a07e6a1b9 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 10:35:52 +0300 Subject: [PATCH 02/23] Fix bib --- joss/paper.bib | 5 ----- 1 file changed, 5 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index f4c30d4..0e15f3f 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -8,11 +8,6 @@ @article{Ravasi:2020 url = {https://www.sciencedirect.com/science/article/pii/S2352711019301086} } - ------ - - - @article{Pearson:2017, url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P}, Archiveprefix = {arXiv}, From f4727008492347a511d9d3042849f38fd68f3590 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 10:39:26 +0300 Subject: [PATCH 03/23] Back to template --- joss/paper.bib | 10 --- joss/paper.md | 188 +++++++++++++++++++------------------------------ 2 files changed, 74 insertions(+), 124 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index 0e15f3f..72e3977 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -1,13 +1,3 @@ -@article{Ravasi:2020, - author = {M. Ravasi and I. Vasconcelos}, - title = "{PyLops - A linear-operator Python library for scalable algebra and optimization}", - journal = {SoftwareX}, - year = 2020, - volume = 11, - doi = {10.1016/j.softx.2019.100361}, - url = {https://www.sciencedirect.com/science/article/pii/S2352711019301086} -} - @article{Pearson:2017, url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P}, Archiveprefix = {arXiv}, diff --git a/joss/paper.md b/joss/paper.md index 2655d72..657f416 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -1,132 +1,92 @@ --- -title: 'PyProximal - scalable convex optimization in Python' +title: 'Gala: A Python package for galactic dynamics' tags: - Python - - optimization - - proximal + - astronomy + - dynamics + - galactic dynamics + - milky way authors: - - name: Matteo Ravasi - orcid: 0000-0003-0020-2721 + - name: Adrian M. Price-Whelan + orcid: 0000-0000-0000-0000 + equal-contrib: true + affiliation: "1, 2" # (Multiple affiliations must be quoted) + - name: Author Without ORCID + equal-contrib: true # (This is how you can denote equal contributions between multiple authors) + affiliation: 2 + - name: Author with no affiliation corresponding: true # (This is how to denote the corresponding author) - affiliation: "1" # (Multiple affiliations must be quoted) + affiliation: 3 + - given-names: Ludwig + dropping-particle: van + surname: Beethoven + affiliation: 3 affiliations: - - name: Earth Science and Engineering, Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia - index: 1 -date: 19 December 2023 + - name: Lyman Spitzer, Jr. Fellow, Princeton University, USA + index: 1 + - name: Institution Name, Country + index: 2 + - name: Independent Researcher, Country + index: 3 +date: 13 August 2017 bibliography: paper.bib - +# Optional fields if submitting to a AAS journal too, see this blog post: +# https://blog.joss.theoj.org/2018/12/a-new-collaboration-with-aas-publishing +aas-doi: 10.3847/xxxxx <- update this with the DOI from AAS once you know it. +aas-journal: Astrophysical Journal <- The name of the AAS journal. +--- # Summary -A broad class of problems in scientific disciplines ranging from image processing and astrophysics, -to geophysics and medical imaging call for the optimization of convex, non-smooth objective functions. -PyProximal is a Python-based library providing users with an extensive suite of state-of-the-art proximal -operators and algorithms. - -Whereas practitioners are usually very familiar with gradient-based optimization and the associated -first- or second-order iterative schemes commonly used to solve unconstrained, smooth optimization problems, proximal -algorithms can be viewed as analogous tools for non-smooth and possibly constrained versions of such problems. These -algorithms sit at a higher level of abstraction than classical algorithms like steepest descent or Newton’s method and -require a basic operation to be performed at each iteration: the evaluation of the so-called proximal operator of the -functional to be optimized. - -In summary, PyProximal aims to democratize the application of convex optimization to scientific problems, providing -users with all the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, -convex objective functions in a high-level, abstract fashion, shielding them away from any unneeded mathematical and -implementation details. - +The forces on stars, galaxies, and dark matter under external gravitational +fields lead to the dynamical evolution of structures in the universe. The orbits +of these bodies are therefore key to understanding the formation, history, and +future state of galaxies. The field of "galactic dynamics," which aims to model +the gravitating components of galaxies to study their structure and evolution, +is now well-established, commonly taught, and frequently used in astronomy. +Aside from toy problems and demonstrations, the majority of problems require +efficient numerical tools, many of which require the same base code (e.g., for +performing numerical orbit integration). # Statement of need -`PyProximal` is a NUMFOCUS-affiliated Python package for convex optimization developed as an integral part of the `PyLops` framework. -It provides practitioners in a variety of scientific disciplines with an easy-to-use Python based framework to -define and solve composite convex objective functions arising in many modern inverse problems. Its API was -designed to provide a class-based and user-friendly interface to proximal operators coupled with function-based -optimizers; because of its modular design, researchers in the field of convex optimization can also benefit from this -package when developing new algorithms in a number of ways: first, they can easily include their newly developed proximal operators -and solvers; second, they can compare these methods with state-of-the-art algorithms already provided in the package - -`PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], our main package for matrix-free linear algebra -and optimization. More specifically, some of `PyLops`'s linear operators and solvers used leveraged in the implementation -of proximal operators that require access to linear operators (e.g., numerical derivatives) and least-squares solvers -(e.g., conjugate gradient). Whilst other similar packages exist in the Python ecosystem, their design usually leads to a -tight coupling between linear operators and solvers and proximal operators and solvers. On the other hand, by following the -Separation of Concerns (SoC) design principle, we reduce to a minimum the overlap between the two libraries, easing both -their development and maintenance, as well as allowing newcomers to learn how to solve inverse problems in a step-by-step manner. -As such, `PyProximal` can be ultimately described as a light-weight extension of `PyLops` that users of the former can very easily -learn and use in short time and with minimal additional effort. - -`PyProximal` was designed to be used by both researchers and students in applied mathematics and engineering courses. -It has already been featured in a number of scientific publications [XX] and in a graduate-level course on inverse problems [XX]. -As the adoption of the library grows across many disciplies, we believe that `PyProximal` will enable exciting scientific discoveries -in a variety of scientific problems with societal impact. - - -# Mathematical framework - -Convex optimization is routinely used to solve problems of the form: - -\begin{equation} -\label{eq:problem} -min_\mathbf{x} f(\mathbf{x}) +g(\mathbf{Ax}) +`Gala` is an Astropy-affiliated Python package for galactic dynamics. Python +enables wrapping low-level languages (e.g., C) for speed without losing +flexibility or ease-of-use in the user-interface. The API for `Gala` was +designed to provide a class-based and user-friendly interface to fast (C or +Cython-optimized) implementations of common operations such as gravitational +potential and force evaluation, orbit integration, dynamical transformations, +and chaos indicators for nonlinear dynamics. `Gala` also relies heavily on and +interfaces well with the implementations of physical units and astronomical +coordinate systems in the `Astropy` package [@astropy] (`astropy.units` and +`astropy.coordinates`). + +`Gala` was designed to be used by both astronomical researchers and by +students in courses on gravitational dynamics or astronomy. It has already been +used in a number of scientific publications [@Pearson:2017] and has also been +used in graduate courses on Galactic dynamics to, e.g., provide interactive +visualizations of textbook material [@Binney:2008]. The combination of speed, +design, and support for Astropy functionality in `Gala` will enable exciting +scientific explorations of forthcoming data releases from the *Gaia* mission +[@gaia] by students and experts alike. + +# Mathematics + +Single dollars ($) are required for inline mathematics e.g. $f(x) = e^{\pi/x}$ + +Double dollars make self-standing equations: + +$$\Theta(x) = \left\{\begin{array}{l} +0\textrm{ if } x < 0\cr +1\textrm{ else} +\end{array}\right.$$ + +You can also use plain \LaTeX for equations +\begin{equation}\label{eq:fourier} +\hat f(\omega) = \int_{-\infty}^{\infty} f(x) e^{i\omega x} dx \end{equation} - -where $f$ and $g$ are possibly non-smooth convex functionals and $\mathbf{A}$ is a linear operator. A special case, -appearing in many scientific applications, is represented by f=1/2 \Vert y - \mathbf{Gx}\Vert_2^2, which identifies -the so-called data misfit term. Here, $\mathbf{G}$ is the modeling operator representing the underlying physical -process the links the unknown model vector $\mathbf{x}$ to the vector of observations $\mathbf{d}$. In this case, -we usually refer to g as the regularization term, where one or multiple terms are added to the objective function to -promote certain features in the sought after solution and/or constraint it within a given set of allowed solutions. - -Independently from the algorithm used to optimize such a cost function, a common feature of all proximal algorithms is -represented by the fact that one must be able to repeatedly evaluate the proximal operator of f and/or g. The proximal -operator of a function f is defined as -… -Whilst evaluating a proximal operator does itself require solving an optimization problem, these subproblems often -admit closed form solutions or can be solved very quickly with ad-hoc specialized methods. Several of such proximal -operators are efficiently implemented in the PyProximal library. - -Finally, there exists three main families of proximal algorithms that can be used to solve various flavors of equation -\autoref{eq:problem} , namely: - -- Proximal gradient method: this method, also commonly referred to as the FBS algorithm red, is usually the - preferred choice when A=I (I.e. identity). Accelerated versions such as the FISTA and TWist algorithms exist - and are usually preferred to the vanilla FBS method; -- Alternating direction of multipliers: this method is based on the well-known splitting strategy and can be used - for a broader class of problem than FBS and its accelarated versions. … -- Primal-dual: another popular algorithm able to tackle the generic problem in equation 1 with any choice of A. - It reformulates the original problem into its primal-dual version of solves a saddle optimization problem. - -# Code structure - -# Pedagogic example - -Let's begin with a simple example showing how to compute the proximal operator of the L1 norm of a vector: - -import numpy as np -from pyproximal import L1 - -l1 = L1() -x = np.arange(-5, 5, 0.1) -xp = l1.prox(x, 1) - -As shown in line 4, one first initialized the operator. Subsequently, the prox method can be invoked to compute the proximal on a vector x with a given tau (here tau=1.). Note that this is a common pattern for all proximal operators in PyProximal - -Moving on, we can how see how such a proximal operator can be used to solve a basic denoising problem of the form: - - -# Research applications - -PyProximal has already been featured in a number of scientific publications: - -- Joint inversion and segmentation of subsurface models: when inverting geophysical data for subsurface priorities, - a prior information that we would like to include in the inversion process is represented by the presence of a - discrete number of rock units, which can be parametrized in terms of their expected mean (or most likely value). - Ravasi and Birnie (2022) framed such a problem as a joint inversion and segmentation where the underlying optimization - is solved in alternating fashion using the Primal-dual algorithm. -- Plug-and-Play (PnP) priors: introduced in 2013 by Vent, in the PnP framework any proximal operator is interpreted - as a denoising problem and solved by means of any statistical or deep learning based denoiser. Recently, Romero +and refer to \autoref{eq:fourier} from text. # Citations From 78a84e6151b1f616dcca30600c0dadbef47dd009 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 10:45:28 +0300 Subject: [PATCH 04/23] Added title and summary --- joss/paper.md | 64 ++++++++++++++++++++------------------------------- 1 file changed, 25 insertions(+), 39 deletions(-) diff --git a/joss/paper.md b/joss/paper.md index 657f416..43f0d7d 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -1,53 +1,39 @@ --- -title: 'Gala: A Python package for galactic dynamics' +title: 'PyProximal - scalable convex optimization in Python' tags: - Python - - astronomy - - dynamics - - galactic dynamics - - milky way + - convex optimization + - proximal authors: - - name: Adrian M. Price-Whelan - orcid: 0000-0000-0000-0000 - equal-contrib: true - affiliation: "1, 2" # (Multiple affiliations must be quoted) - - name: Author Without ORCID - equal-contrib: true # (This is how you can denote equal contributions between multiple authors) - affiliation: 2 - - name: Author with no affiliation + - name: Matteo Ravasi + orcid: 0000-0003-0020-2721 corresponding: true # (This is how to denote the corresponding author) - affiliation: 3 - - given-names: Ludwig - dropping-particle: van - surname: Beethoven - affiliation: 3 + affiliation: 1 # (Multiple affiliations must be quoted) affiliations: - - name: Lyman Spitzer, Jr. Fellow, Princeton University, USA - index: 1 - - name: Institution Name, Country - index: 2 - - name: Independent Researcher, Country - index: 3 -date: 13 August 2017 + - name: Earth Science and Engineering, Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia + index: 1 +date: 19 December 2023 bibliography: paper.bib - -# Optional fields if submitting to a AAS journal too, see this blog post: -# https://blog.joss.theoj.org/2018/12/a-new-collaboration-with-aas-publishing -aas-doi: 10.3847/xxxxx <- update this with the DOI from AAS once you know it. -aas-journal: Astrophysical Journal <- The name of the AAS journal. --- # Summary -The forces on stars, galaxies, and dark matter under external gravitational -fields lead to the dynamical evolution of structures in the universe. The orbits -of these bodies are therefore key to understanding the formation, history, and -future state of galaxies. The field of "galactic dynamics," which aims to model -the gravitating components of galaxies to study their structure and evolution, -is now well-established, commonly taught, and frequently used in astronomy. -Aside from toy problems and demonstrations, the majority of problems require -efficient numerical tools, many of which require the same base code (e.g., for -performing numerical orbit integration). +A broad class of problems in scientific disciplines ranging from image processing and astrophysics, +to geophysics and medical imaging call for the optimization of convex, non-smooth objective functions. +PyProximal is a Python-based library providing users with an extensive suite of state-of-the-art proximal +operators and algorithms. + +Whereas practitioners are usually very familiar with gradient-based optimization and the associated +first- or second-order iterative schemes commonly used to solve unconstrained, smooth optimization problems, proximal +algorithms can be viewed as analogous tools for non-smooth and possibly constrained versions of such problems. These +algorithms sit at a higher level of abstraction than classical algorithms like steepest descent or Newton’s method and +require a basic operation to be performed at each iteration: the evaluation of the so-called proximal operator of the +functional to be optimized. + +In summary, PyProximal aims to democratize the application of convex optimization to scientific problems, providing +users with all the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, +convex objective functions in a high-level, abstract fashion, shielding them away from any unneeded mathematical and +implementation details. # Statement of need From 8bb8565eb566a5ec3460a108f6901fe4fa7252ab Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 10:48:08 +0300 Subject: [PATCH 05/23] Added statement of need --- joss/paper.bib | 10 ++++++++++ joss/paper.md | 39 +++++++++++++++++++++++---------------- 2 files changed, 33 insertions(+), 16 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index 72e3977..f5833c6 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -56,4 +56,14 @@ @misc{fidgit publisher = {GitHub}, journal = {GitHub repository}, url = {https://github.com/arfon/fidgit} +} + +@article{Ravasi:2020, + author = {M. Ravasi and I. Vasconcelos}, + title = "{PyLops - A linear-operator Python library for scalable algebra and optimization}", + journal = {SoftwareX}, + year = 2020, + volume = 11, + doi = {10.1016/j.softx.2019.100361}, + url = {https://www.sciencedirect.com/science/article/pii/S2352711019301086} } \ No newline at end of file diff --git a/joss/paper.md b/joss/paper.md index 43f0d7d..96cfb77 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -18,22 +18,29 @@ bibliography: paper.bib # Summary -A broad class of problems in scientific disciplines ranging from image processing and astrophysics, -to geophysics and medical imaging call for the optimization of convex, non-smooth objective functions. -PyProximal is a Python-based library providing users with an extensive suite of state-of-the-art proximal -operators and algorithms. - -Whereas practitioners are usually very familiar with gradient-based optimization and the associated -first- or second-order iterative schemes commonly used to solve unconstrained, smooth optimization problems, proximal -algorithms can be viewed as analogous tools for non-smooth and possibly constrained versions of such problems. These -algorithms sit at a higher level of abstraction than classical algorithms like steepest descent or Newton’s method and -require a basic operation to be performed at each iteration: the evaluation of the so-called proximal operator of the -functional to be optimized. - -In summary, PyProximal aims to democratize the application of convex optimization to scientific problems, providing -users with all the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, -convex objective functions in a high-level, abstract fashion, shielding them away from any unneeded mathematical and -implementation details. +`PyProximal` is a NUMFOCUS-affiliated Python package for convex optimization developed as an integral part of the `PyLops` framework. +It provides practitioners in a variety of scientific disciplines with an easy-to-use Python based framework to +define and solve composite convex objective functions arising in many modern inverse problems. Its API was +designed to provide a class-based and user-friendly interface to proximal operators coupled with function-based +optimizers; because of its modular design, researchers in the field of convex optimization can also benefit from this +package when developing new algorithms in a number of ways: first, they can easily include their newly developed proximal operators +and solvers; second, they can compare these methods with state-of-the-art algorithms already provided in the package + +`PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], our main package for matrix-free linear algebra +and optimization. More specifically, some of `PyLops`'s linear operators and solvers used leveraged in the implementation +of proximal operators that require access to linear operators (e.g., numerical derivatives) and least-squares solvers +(e.g., conjugate gradient). Whilst other similar packages exist in the Python ecosystem, their design usually leads to a +tight coupling between linear operators and solvers and proximal operators and solvers. On the other hand, by following the +Separation of Concerns (SoC) design principle, we reduce to a minimum the overlap between the two libraries, easing both +their development and maintenance, as well as allowing newcomers to learn how to solve inverse problems in a step-by-step manner. +As such, `PyProximal` can be ultimately described as a light-weight extension of `PyLops` that users of the former can very easily +learn and use in short time and with minimal additional effort. + +`PyProximal` was designed to be used by both researchers and students in applied mathematics and engineering courses. +It has already been featured in a number of scientific publications XX and in a graduate-level course on inverse problems XX. +As the adoption of the library grows across many disciplies, we believe that `PyProximal` will enable exciting scientific discoveries +in a variety of scientific problems with societal impact. + # Statement of need From 453911aef6bb1d3c8cbe1c402792dd5c7ba05fe2 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 10:58:01 +0300 Subject: [PATCH 06/23] Add math framework --- joss/paper.md | 72 +++++++++++++++++++++++++-------------------------- 1 file changed, 35 insertions(+), 37 deletions(-) diff --git a/joss/paper.md b/joss/paper.md index 96cfb77..f93ab49 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -18,6 +18,26 @@ bibliography: paper.bib # Summary +A broad class of problems in scientific disciplines ranging from image processing and astrophysics, +to geophysics and medical imaging call for the optimization of convex, non-smooth objective functions. +PyProximal is a Python-based library providing users with an extensive suite of state-of-the-art proximal +operators and algorithms. + +Whereas practitioners are usually very familiar with gradient-based optimization and the associated +first- or second-order iterative schemes commonly used to solve unconstrained, smooth optimization problems, proximal +algorithms can be viewed as analogous tools for non-smooth and possibly constrained versions of such problems. These +algorithms sit at a higher level of abstraction than classical algorithms like steepest descent or Newton’s method and +require a basic operation to be performed at each iteration: the evaluation of the so-called proximal operator of the +functional to be optimized. + +In summary, PyProximal aims to democratize the application of convex optimization to scientific problems, providing +users with all the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, +convex objective functions in a high-level, abstract fashion, shielding them away from any unneeded mathematical and +implementation details. + + +# Statement of need + `PyProximal` is a NUMFOCUS-affiliated Python package for convex optimization developed as an integral part of the `PyLops` framework. It provides practitioners in a variety of scientific disciplines with an easy-to-use Python based framework to define and solve composite convex objective functions arising in many modern inverse problems. Its API was @@ -39,47 +59,25 @@ learn and use in short time and with minimal additional effort. `PyProximal` was designed to be used by both researchers and students in applied mathematics and engineering courses. It has already been featured in a number of scientific publications XX and in a graduate-level course on inverse problems XX. As the adoption of the library grows across many disciplies, we believe that `PyProximal` will enable exciting scientific discoveries -in a variety of scientific problems with societal impact. +in a variety of scientific problems with societal impact. -# Statement of need +# Mathematical framework -`Gala` is an Astropy-affiliated Python package for galactic dynamics. Python -enables wrapping low-level languages (e.g., C) for speed without losing -flexibility or ease-of-use in the user-interface. The API for `Gala` was -designed to provide a class-based and user-friendly interface to fast (C or -Cython-optimized) implementations of common operations such as gravitational -potential and force evaluation, orbit integration, dynamical transformations, -and chaos indicators for nonlinear dynamics. `Gala` also relies heavily on and -interfaces well with the implementations of physical units and astronomical -coordinate systems in the `Astropy` package [@astropy] (`astropy.units` and -`astropy.coordinates`). - -`Gala` was designed to be used by both astronomical researchers and by -students in courses on gravitational dynamics or astronomy. It has already been -used in a number of scientific publications [@Pearson:2017] and has also been -used in graduate courses on Galactic dynamics to, e.g., provide interactive -visualizations of textbook material [@Binney:2008]. The combination of speed, -design, and support for Astropy functionality in `Gala` will enable exciting -scientific explorations of forthcoming data releases from the *Gaia* mission -[@gaia] by students and experts alike. - -# Mathematics - -Single dollars ($) are required for inline mathematics e.g. $f(x) = e^{\pi/x}$ - -Double dollars make self-standing equations: - -$$\Theta(x) = \left\{\begin{array}{l} -0\textrm{ if } x < 0\cr -1\textrm{ else} -\end{array}\right.$$ - -You can also use plain \LaTeX for equations -\begin{equation}\label{eq:fourier} -\hat f(\omega) = \int_{-\infty}^{\infty} f(x) e^{i\omega x} dx +Convex optimization is routinely used to solve problems of the form: + +\begin{equation} +\label{eq:problem} +\argmin_\mathbf{x} f(\mathbf{x}) +g(\mathbf{Lx}) \end{equation} -and refer to \autoref{eq:fourier} from text. + +where $f$ and $g$ are possibly non-smooth convex functionals and $\mathbf{A}$ is a linear operator. A special case, +appearing in many scientific applications, is represented by $f=1/2 \Vert y - \mathcal{A}(\mathbf{x})\Vert_2^2$, which identifies +the so-called data misfit term. Here, $\mathcal{A}$ is a (possibly non-linear) modeling operator representing the underlying physical +process the links the unknown model vector $\mathbf{x}$ to the vector of observations $\mathbf{y}$. In this case, +we usually refer to $g$ as the regularization term, where one or multiple terms are added to the objective function to +promote certain features in the sought after solution and/or constraint the optimization process to produce a solution +within a given set of allowed vectors. # Citations From 160201511caa608afaffbe55ea6ec6950ddcfef7 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 10:59:18 +0300 Subject: [PATCH 07/23] Add math framework --- joss/paper.md | 1 - 1 file changed, 1 deletion(-) diff --git a/joss/paper.md b/joss/paper.md index f93ab49..dd825c4 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -61,7 +61,6 @@ It has already been featured in a number of scientific publications XX and in a As the adoption of the library grows across many disciplies, we believe that `PyProximal` will enable exciting scientific discoveries in a variety of scientific problems with societal impact. - # Mathematical framework Convex optimization is routinely used to solve problems of the form: From 42b1c1baea643888e8841c848674ab978736f55e Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 11:01:07 +0300 Subject: [PATCH 08/23] Fix math framework --- joss/paper.md | 9 +-------- 1 file changed, 1 insertion(+), 8 deletions(-) diff --git a/joss/paper.md b/joss/paper.md index dd825c4..fff0866 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -67,16 +67,9 @@ Convex optimization is routinely used to solve problems of the form: \begin{equation} \label{eq:problem} -\argmin_\mathbf{x} f(\mathbf{x}) +g(\mathbf{Lx}) +\min_\mathbf{x} f(\mathbf{x}) +g(\mathbf{Lx}) \end{equation} -where $f$ and $g$ are possibly non-smooth convex functionals and $\mathbf{A}$ is a linear operator. A special case, -appearing in many scientific applications, is represented by $f=1/2 \Vert y - \mathcal{A}(\mathbf{x})\Vert_2^2$, which identifies -the so-called data misfit term. Here, $\mathcal{A}$ is a (possibly non-linear) modeling operator representing the underlying physical -process the links the unknown model vector $\mathbf{x}$ to the vector of observations $\mathbf{y}$. In this case, -we usually refer to $g$ as the regularization term, where one or multiple terms are added to the objective function to -promote certain features in the sought after solution and/or constraint the optimization process to produce a solution -within a given set of allowed vectors. # Citations From b1a02939c948aebd829b1781e6c5bebadfcb446d Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 14:22:00 +0300 Subject: [PATCH 09/23] Added more in math section --- joss/paper.md | 43 +++++++++++-------------------------------- 1 file changed, 11 insertions(+), 32 deletions(-) diff --git a/joss/paper.md b/joss/paper.md index fff0866..32bcb96 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -56,10 +56,6 @@ their development and maintenance, as well as allowing newcomers to learn how to As such, `PyProximal` can be ultimately described as a light-weight extension of `PyLops` that users of the former can very easily learn and use in short time and with minimal additional effort. -`PyProximal` was designed to be used by both researchers and students in applied mathematics and engineering courses. -It has already been featured in a number of scientific publications XX and in a graduate-level course on inverse problems XX. -As the adoption of the library grows across many disciplies, we believe that `PyProximal` will enable exciting scientific discoveries -in a variety of scientific problems with societal impact. # Mathematical framework @@ -70,33 +66,16 @@ Convex optimization is routinely used to solve problems of the form: \min_\mathbf{x} f(\mathbf{x}) +g(\mathbf{Lx}) \end{equation} - -# Citations - -Citations to entries in paper.bib should be in -[rMarkdown](http://rmarkdown.rstudio.com/authoring_bibliographies_and_citations.html) -format. - -If you want to cite a software repository URL (e.g. something on GitHub without a preferred -citation) then you can do it with the example BibTeX entry below for @fidgit. - -For a quick reference, the following citation commands can be used: -- `@author:2001` -> "Author et al. (2001)" -- `[@author:2001]` -> "(Author et al., 2001)" -- `[@author1:2001; @author2:2001]` -> "(Author1 et al., 2001; Author2 et al., 2002)" - -# Figures - -Figures can be included like this: -![Caption for example figure.\label{fig:example}](figure.png) -and referenced from text using \autoref{fig:example}. - -Figure sizes can be customized by adding an optional second parameter: -![Caption for example figure.](figure.png){ width=20% } - -# Acknowledgements - -We acknowledge contributions from Brigitta Sipocz, Syrtis Major, and Semyeong -Oh, and support from Kathryn Johnston during the genesis of this project. +where $f$ and $g$ are possibly non-smooth convex functionals and $\mathbf{A}$ is a linear operator. A special case, +appearing in many scientific applications, is represented by $f=1/2 \Vert y - \mathcal{A}(\mathbf{x})\Vert_2^2$, which identifies +the so-called data misfit term. Here, $\mathcal{A}$ is a (possibly non-linear) modeling operator representing the underlying physical +process the links the unknown model vector $\mathbf{x}$ to the vector of observations $\mathbf{y}$. In this case, +we usually refer to $g$ as the regularization term, where one or multiple terms are added to the objective function to +promote certain features in the sought after solution and/or constraint the optimization process to produce a solution +within a given set of allowed vectors. + +Independent on the algorithm used to optimize such a cost function, a common feature of all proximal algorithms is +represented by the fact that one must be able to repeatedly evaluate the proximal operator of $f$ and/or $g$. The proximal +operator of a function $f$ is defined as # References \ No newline at end of file From c000b7d6e209f9074c2755579a22a39dc72097c0 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 14:26:37 +0300 Subject: [PATCH 10/23] Finished math section --- joss/paper.md | 22 +++++++++++++++++++++- 1 file changed, 21 insertions(+), 1 deletion(-) diff --git a/joss/paper.md b/joss/paper.md index 32bcb96..d324e60 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -59,7 +59,7 @@ learn and use in short time and with minimal additional effort. # Mathematical framework -Convex optimization is routinely used to solve problems of the form: +Convex optimization is routinely used to solve problems of the form [@Parikh:2013]: \begin{equation} \label{eq:problem} @@ -78,4 +78,24 @@ Independent on the algorithm used to optimize such a cost function, a common fea represented by the fact that one must be able to repeatedly evaluate the proximal operator of $f$ and/or $g$. The proximal operator of a function $f$ is defined as + +Whilst evaluating a proximal operator does itself require solving an optimization problem, these subproblems often +admit closed form solutions or can be solved very quickly with ad-hoc specialized methods. Several of such proximal +operators are efficiently implemented in the ``PyProximal`` library. + +Finally, there exists three main families of proximal algorithms that can be used to solve various flavors of equation +\autoref{eq:problem}, namely: + +- Proximal gradient method: this method, also commonly referred to as the FBS algorithm red, is usually the + preferred choice when $A=I$ (i.e. identity operator). Accelerated versions such as the FISTA and TWist algorithms exist + and are usually preferred to the vanilla FBS method; +- Alternating direction of multipliers: this method is based on the well-known splitting strategy and can be used + for a broader class of problem than FBS and its accelarated versions. … +- Primal-dual: another popular algorithm able to tackle the generic problem in equation 1 with any choice of A. + It reformulates the original problem into its primal-dual version of solves a saddle optimization problem. + +``PyProximal`` provides implementations for these three families of algorithms; moreover, our solvers include additional features +such as back-tracking for automatic selection of step-sizes, logging of cost function evolution, and custom callbacks. + + # References \ No newline at end of file From e2169692a11202e1f1d520588b25142ced319052 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 15:19:35 +0300 Subject: [PATCH 11/23] Add code section --- 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zRTJ~fWiUqif6T+Qzg@_af$#46SYCcI=&M>mNNQ>-f8|Q_edSLd_qqW{R>PyC8bOfe zbdvRg_#d@E&WWzzWGjdf3Q-4CQ&4Aj!-?(=OQYDFlJh1fM^R(?TK#dz zjuj9{ib%HR*&)X1q(aiN@+jYETZ&i4N`{vT45Yl0 zw8w`P=yOA#(xwx>U|9cpap6g{*cxScW~8zz4ra|-;b6A^PeDA z?BhQ{{3nPXL&bj<@t;Nff3}F*);Qb(R?S0q@&|;#^whaJ8bwidoFm#OP3lkd?`kKs Ll+%t~`s4oq3bqwC literal 0 HcmV?d00001 diff --git a/joss/paper.md b/joss/paper.md index d324e60..955086b 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -78,6 +78,11 @@ Independent on the algorithm used to optimize such a cost function, a common fea represented by the fact that one must be able to repeatedly evaluate the proximal operator of $f$ and/or $g$. The proximal operator of a function $f$ is defined as +\begin{equation} +\label{eq:prox} +prox_{\tau f} (\mathbf{x}) = \argmin_{\mathbf{y}} f(\mathbf{y}) + + \frac{1}{2 \tau}||\mathbf{y} - \mathbf{x}||^2_2 +\end{equation} Whilst evaluating a proximal operator does itself require solving an optimization problem, these subproblems often admit closed form solutions or can be solved very quickly with ad-hoc specialized methods. Several of such proximal @@ -98,4 +103,14 @@ Finally, there exists three main families of proximal algorithms that can be use such as back-tracking for automatic selection of step-sizes, logging of cost function evolution, and custom callbacks. +# Code structure + +``PyProximal`` aims to provide a modular, and easy-to-use Application Programming Interface (API) that scientists +can use to define and solve convex objective functions by means of proximal algorithms. + +The API is composed of two interconnected units as shown in Fig. 1. + +![Schematic representation of the ``PyProximal`` API.](figs/software.png){ width=70% } + + # References \ No newline at end of file From 5fa749db395d3c60705f0ebe7d09b3a65491e5e1 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 15:20:44 +0300 Subject: [PATCH 12/23] Fix equation --- joss/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/joss/paper.md b/joss/paper.md index 955086b..89fc3f0 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -80,7 +80,7 @@ operator of a function $f$ is defined as \begin{equation} \label{eq:prox} -prox_{\tau f} (\mathbf{x}) = \argmin_{\mathbf{y}} f(\mathbf{y}) + +prox_{\tau f} (\mathbf{x}) = \min_{\mathbf{y}} f(\mathbf{y}) + \frac{1}{2 \tau}||\mathbf{y} - \mathbf{x}||^2_2 \end{equation} From 1549385e4da6b04504010e9fd19cd3ddba1e5cdf Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 15:45:24 +0300 Subject: [PATCH 13/23] Add refs --- joss/paper.bib | 87 ++++++++++++++++---------------------------------- joss/paper.md | 24 +++++++++----- 2 files changed, 43 insertions(+), 68 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index f5833c6..d128e08 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -1,63 +1,3 @@ -@article{Pearson:2017, - url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P}, - Archiveprefix = {arXiv}, - Author = {{Pearson}, S. and {Price-Whelan}, A.~M. and {Johnston}, K.~V.}, - Eprint = {1703.04627}, - Journal = {ArXiv e-prints}, - Keywords = {Astrophysics - Astrophysics of Galaxies}, - Month = mar, - Title = {{Gaps in Globular Cluster Streams: Pal 5 and the Galactic Bar}}, - Year = 2017 -} - -@book{Binney:2008, - url = {http://adsabs.harvard.edu/abs/2008gady.book.....B}, - Author = {{Binney}, J. and {Tremaine}, S.}, - Booktitle = {Galactic Dynamics: Second Edition, by James Binney and Scott Tremaine.~ISBN 978-0-691-13026-2 (HB).~Published by Princeton University Press, Princeton, NJ USA, 2008.}, - Publisher = {Princeton University Press}, - Title = {{Galactic Dynamics: Second Edition}}, - Year = 2008 -} - -@article{gaia, - author = {{Gaia Collaboration}}, - title = "{The Gaia mission}", - journal = {Astronomy and Astrophysics}, - archivePrefix = "arXiv", - eprint = {1609.04153}, - primaryClass = "astro-ph.IM", - keywords = {space vehicles: instruments, Galaxy: structure, astrometry, parallaxes, proper motions, telescopes}, - year = 2016, - month = nov, - volume = 595, - doi = {10.1051/0004-6361/201629272}, - url = {http://adsabs.harvard.edu/abs/2016A%26A...595A...1G}, -} - -@article{astropy, - author = {{Astropy Collaboration}}, - title = "{Astropy: A community Python package for astronomy}", - journal = {Astronomy and Astrophysics}, - archivePrefix = "arXiv", - eprint = {1307.6212}, - primaryClass = "astro-ph.IM", - keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools}, - year = 2013, - month = oct, - volume = 558, - doi = {10.1051/0004-6361/201322068}, - url = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A} -} - -@misc{fidgit, - author = {A. M. Smith and K. Thaney and M. Hahnel}, - title = {Fidgit: An ungodly union of GitHub and Figshare}, - year = {2020}, - publisher = {GitHub}, - journal = {GitHub repository}, - url = {https://github.com/arfon/fidgit} -} - @article{Ravasi:2020, author = {M. Ravasi and I. Vasconcelos}, title = "{PyLops - A linear-operator Python library for scalable algebra and optimization}", @@ -66,4 +6,31 @@ @article{Ravasi:2020 volume = 11, doi = {10.1016/j.softx.2019.100361}, url = {https://www.sciencedirect.com/science/article/pii/S2352711019301086} +} + +@book{Parikh:2013, + url = {https://web.stanford.edu/~boyd/papers/pdf/prox_algs.pdf}, + Author = {N. Parikh}, + Booktitle = {Proximal Algorithms}, + Publisher = {Foundations and Trends in Optimization}, + Year = 2013 +} + +@book{Combettes:2011, + url = {https://link.springer.com/chapter/10.1007/978-1-4419-9569-8_10}, + Author = {P. Combettes and J.-C. Pesquet}, + Booktitle = {Fixed-Point Algorithms for Inverse Problems in Science and Engineering.}, + Publisher = {Springer Optimization and Its Applications}, + Title = {Proximal splitting methods in signal processing}, + Year = 2011 +} + +@article{Boyd:2011, + author = {S. Boyd and N. Parikh and E. Chu and B. Peleato and J. Eckstein}, + title = "{Distributed optimization and statistical learning via the alternating direction method of multipliers}", + journal = {Foundations and Trends in Machine Learning}, + year = 2011, + volume = 3, + doi = {10.1561/2200000016}, + url = {https://web.stanford.edu/~boyd/papers/pdf/admm_distr_stats.pdf} } \ No newline at end of file diff --git a/joss/paper.md b/joss/paper.md index 89fc3f0..20697ab 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -91,11 +91,11 @@ operators are efficiently implemented in the ``PyProximal`` library. Finally, there exists three main families of proximal algorithms that can be used to solve various flavors of equation \autoref{eq:problem}, namely: -- Proximal gradient method: this method, also commonly referred to as the FBS algorithm red, is usually the - preferred choice when $A=I$ (i.e. identity operator). Accelerated versions such as the FISTA and TWist algorithms exist - and are usually preferred to the vanilla FBS method; -- Alternating direction of multipliers: this method is based on the well-known splitting strategy and can be used - for a broader class of problem than FBS and its accelarated versions. … +- Proximal gradient method [@Combettes:2011]: this method, also commonly referred to as the Forward-Backward Splitting (FBS) + algorithm, is usually the preferred choice when $\mathbf{L}=\mathbf{I}$ (i.e. identity operator). Accelerated versions such + as the FISTA and TwIST algorithms exist and are usually preferred to the vanilla FBS method; +- Alternating Direction Method of Multipliers [@Boyd:2011]: this method is based on the well-known splitting strategy and can be used + for a broader class of problem than FBS and its accelerated versions. - Primal-dual: another popular algorithm able to tackle the generic problem in equation 1 with any choice of A. It reformulates the original problem into its primal-dual version of solves a saddle optimization problem. @@ -106,11 +106,19 @@ such as back-tracking for automatic selection of step-sizes, logging of cost fun # Code structure ``PyProximal`` aims to provide a modular, and easy-to-use Application Programming Interface (API) that scientists -can use to define and solve convex objective functions by means of proximal algorithms. +can use to define and solve convex objective functions by means of proximal algorithms. The API is composed of +two main units as shown in Fig. 1. -The API is composed of two interconnected units as shown in Fig. 1. +The first unit contains the entire suite of proximal operators, which are class-based objects that subclass +the ``pylops.ProxOperator`` parent class. For each of these operators, the solution to the proximal optimization +problem in equation \autoref{eq:prox} (and/or the dual proximal problem) is implemented in the ``prox`` +(and/or ``dualprox``) method. As in most cases a closed-form solution exists for such a problem, our +implementation provides users with the most efficient way to evaluate a proximal operator. The second unit comprises +of so-called proximal solvers, optimization algorithms that are suited to solve problems of the form in equation \autoref{eq:problem}. -![Schematic representation of the ``PyProximal`` API.](figs/software.png){ width=70% } + + +![Schematic representation of the ``PyProximal`` API.](figs/software.png){ width=90% } # References \ No newline at end of file From 33983dc9dd63a2ce6244a89ea5d79ef40374548c Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 23:24:00 +0300 Subject: [PATCH 14/23] Shorten summary --- joss/paper.bib | 12 +++++++++++- joss/paper.md | 36 +++++++++++++++++++----------------- 2 files changed, 30 insertions(+), 18 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index d128e08..98cc17a 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -33,4 +33,14 @@ @article{Boyd:2011 volume = 3, doi = {10.1561/2200000016}, url = {https://web.stanford.edu/~boyd/papers/pdf/admm_distr_stats.pdf} -} \ No newline at end of file +} + +@article{Chambolle:2011, + author = {A. Chambolle and T. Pock}, + title = "{A first-order primal-dual algorithm for convex problems with applications to imaging}", + journal = {Journal of Mathematical Imaging and Vision}, + year = 2011, + volume = 40, + doi = {10.1007/s10851-010-0251-1}, + url = {https://link.springer.com/article/10.1007/s10851-010-0251-1} +} diff --git a/joss/paper.md b/joss/paper.md index 20697ab..6244d41 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -20,20 +20,12 @@ bibliography: paper.bib A broad class of problems in scientific disciplines ranging from image processing and astrophysics, to geophysics and medical imaging call for the optimization of convex, non-smooth objective functions. -PyProximal is a Python-based library providing users with an extensive suite of state-of-the-art proximal -operators and algorithms. - -Whereas practitioners are usually very familiar with gradient-based optimization and the associated -first- or second-order iterative schemes commonly used to solve unconstrained, smooth optimization problems, proximal -algorithms can be viewed as analogous tools for non-smooth and possibly constrained versions of such problems. These -algorithms sit at a higher level of abstraction than classical algorithms like steepest descent or Newton’s method and -require a basic operation to be performed at each iteration: the evaluation of the so-called proximal operator of the -functional to be optimized. - -In summary, PyProximal aims to democratize the application of convex optimization to scientific problems, providing -users with all the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, -convex objective functions in a high-level, abstract fashion, shielding them away from any unneeded mathematical and -implementation details. +Whereas practitioners are usually very familiar with gradient-based optimization algorithms, commonly used +to solve unconstrained, smooth optimization problems, proximal algorithms can be viewed as analogous tools for +non-smooth and possibly constrained versions of such problems. PyProximal is a Python-based library aimed at +democratize the application of convex optimization to scientific problems, providing all the required +building blocks (i.e., proximal operators and algorithms) to define and solve complex, convex objective functions +in a high-level, abstract fashion, shielding users away from any unneeded mathematical and implementation details. # Statement of need @@ -91,12 +83,12 @@ operators are efficiently implemented in the ``PyProximal`` library. Finally, there exists three main families of proximal algorithms that can be used to solve various flavors of equation \autoref{eq:problem}, namely: -- Proximal gradient method [@Combettes:2011]: this method, also commonly referred to as the Forward-Backward Splitting (FBS) +- Proximal Gradient [@Combettes:2011]: this method, also commonly referred to as the Forward-Backward Splitting (FBS) algorithm, is usually the preferred choice when $\mathbf{L}=\mathbf{I}$ (i.e. identity operator). Accelerated versions such as the FISTA and TwIST algorithms exist and are usually preferred to the vanilla FBS method; - Alternating Direction Method of Multipliers [@Boyd:2011]: this method is based on the well-known splitting strategy and can be used for a broader class of problem than FBS and its accelerated versions. -- Primal-dual: another popular algorithm able to tackle the generic problem in equation 1 with any choice of A. +- Primal-Dual [@Chambolle:2011]: another popular algorithm able to tackle the generic problem in equation 1 with any choice of A. It reformulates the original problem into its primal-dual version of solves a saddle optimization problem. ``PyProximal`` provides implementations for these three families of algorithms; moreover, our solvers include additional features @@ -116,9 +108,19 @@ problem in equation \autoref{eq:prox} (and/or the dual proximal problem) is impl implementation provides users with the most efficient way to evaluate a proximal operator. The second unit comprises of so-called proximal solvers, optimization algorithms that are suited to solve problems of the form in equation \autoref{eq:problem}. +![Schematic representation of the ``PyProximal`` API.](figs/software.png){ width=90% } +# Representative PyProximal Use Cases -![Schematic representation of the ``PyProximal`` API.](figs/software.png){ width=90% } +PyProximal has already been featured in a number of scientific publications: + +- Joint inversion and segmentation of subsurface models: when inverting geophysical data for subsurface priorities, + a prior information that we would like to include in the inversion process is represented by the presence of a + discrete number of rock units, which can be parametrized in terms of their expected mean (or most likely value). + Ravasi and Birnie (2022) framed such a problem as a joint inversion and segmentation where the underlying optimization + is solved in alternating fashion using the Primal-dual algorithm. +- Plug-and-Play (PnP) priors: introduced in 2013 by Vent, in the PnP framework any proximal operator is interpreted + as a denoising problem and solved by means of any statistical or deep learning based denoiser. Recently, Romero # References \ No newline at end of file From 82549d031648348cd7957bc91641972247a4dceb Mon Sep 17 00:00:00 2001 From: mrava87 Date: Tue, 19 Dec 2023 23:40:02 +0300 Subject: [PATCH 15/23] Shorten stat of intent --- joss/paper.md | 40 ++++++++++++++++++++-------------------- 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/joss/paper.md b/joss/paper.md index 6244d41..b1322c2 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -20,33 +20,33 @@ bibliography: paper.bib A broad class of problems in scientific disciplines ranging from image processing and astrophysics, to geophysics and medical imaging call for the optimization of convex, non-smooth objective functions. -Whereas practitioners are usually very familiar with gradient-based optimization algorithms, commonly used +Whereas practitioners are usually familiar with gradient-based algorithms, commonly used to solve unconstrained, smooth optimization problems, proximal algorithms can be viewed as analogous tools for -non-smooth and possibly constrained versions of such problems. PyProximal is a Python-based library aimed at -democratize the application of convex optimization to scientific problems, providing all the required +non-smooth and possibly constrained versions of such problems. ``PyProximal`` is a Python-based library aimed at +democratizing the application of convex optimization to scientific problems, providing all the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, convex objective functions -in a high-level, abstract fashion, shielding users away from any unneeded mathematical and implementation details. +in a high-level manner, shielding users away from any unneeded mathematical and implementation details. # Statement of need -`PyProximal` is a NUMFOCUS-affiliated Python package for convex optimization developed as an integral part of the `PyLops` framework. -It provides practitioners in a variety of scientific disciplines with an easy-to-use Python based framework to -define and solve composite convex objective functions arising in many modern inverse problems. Its API was -designed to provide a class-based and user-friendly interface to proximal operators coupled with function-based -optimizers; because of its modular design, researchers in the field of convex optimization can also benefit from this -package when developing new algorithms in a number of ways: first, they can easily include their newly developed proximal operators -and solvers; second, they can compare these methods with state-of-the-art algorithms already provided in the package - -`PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], our main package for matrix-free linear algebra -and optimization. More specifically, some of `PyLops`'s linear operators and solvers used leveraged in the implementation -of proximal operators that require access to linear operators (e.g., numerical derivatives) and least-squares solvers -(e.g., conjugate gradient). Whilst other similar packages exist in the Python ecosystem, their design usually leads to a -tight coupling between linear operators and solvers and proximal operators and solvers. On the other hand, by following the -Separation of Concerns (SoC) design principle, we reduce to a minimum the overlap between the two libraries, easing both -their development and maintenance, as well as allowing newcomers to learn how to solve inverse problems in a step-by-step manner. +`PyProximal` is a Python package for convex optimization, developed as an integral part of the `PyLops` framework. +It provides practitioners with an easy-to-use framework to define and solve composite convex objective functions +arising in many modern inverse problems. Its API is designed to offer a class-based and user-friendly interface +to proximal operators, coupled with function-based optimizers; because of its modular design, researchers in the field +of convex optimization can also benefit from this package in a number of ways when developing new algorithms: first, +they can easily include their newly developed proximal operators and solvers; second, they can compare these methods +with state-of-the-art algorithms already provided in the package + +`PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], a Python package for matrix-free linear algebra +and optimization. More specifically, `PyLops` is leveraged in the implementation of proximal operators that require +access to linear operators (e.g., numerical derivatives) and/or least-squares solvers +(e.g., conjugate gradient). Whilst similar packages exist in the Python ecosystem, their design usually leads to a +tight coupling between linear and proximal operators, and their respective solvers. On the other hand, by following the +Separation of Concerns (SoC) design principle, the overlap between `PyLops` and `PyProximal` is reduced to a minimum, easing both +their development and maintenance, as well as allowing newcomers to learn how to solve inverse problems in a step-by-step fashion. As such, `PyProximal` can be ultimately described as a light-weight extension of `PyLops` that users of the former can very easily -learn and use in short time and with minimal additional effort. +learn and use with minimal additional effort. # Mathematical framework From c1af6eb9ddaa0b001d41f90c712ae688644bd660 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Wed, 20 Dec 2023 00:03:34 +0300 Subject: [PATCH 16/23] Started use cases --- joss/paper.bib | 10 ++++++++ joss/paper.md | 63 ++++++++++++++++++++++++++------------------------ 2 files changed, 43 insertions(+), 30 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index 98cc17a..0cc7bbe 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -44,3 +44,13 @@ @article{Chambolle:2011 doi = {10.1007/s10851-010-0251-1}, url = {https://link.springer.com/article/10.1007/s10851-010-0251-1} } + +@article{Ravasi:2022, + author = {M. Ravasi and C. Birnie}, + title = "{A joint inversion-segmentation approach to assisted seismic interpretation}", + journal = {Geophysical Journal International}, + year = 2022, + volume = 228, + doi = {10.1093/gji/ggab388}, + url = {https://academic.oup.com/gji/article/228/2/893/6374557} +} \ No newline at end of file diff --git a/joss/paper.md b/joss/paper.md index b1322c2..45cb7a0 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -22,7 +22,10 @@ A broad class of problems in scientific disciplines ranging from image processin to geophysics and medical imaging call for the optimization of convex, non-smooth objective functions. Whereas practitioners are usually familiar with gradient-based algorithms, commonly used to solve unconstrained, smooth optimization problems, proximal algorithms can be viewed as analogous tools for -non-smooth and possibly constrained versions of such problems. ``PyProximal`` is a Python-based library aimed at +non-smooth and possibly constrained versions of such problems. These +algorithms sit at a higher level of abstraction than gradient-based algorithms and +require a basic operation to be performed at each iteration: the evaluation of the so-called proximal operator of the +functional to be optimized. ``PyProximal`` is a Python-based library aimed at democratizing the application of convex optimization to scientific problems, providing all the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, convex objective functions in a high-level manner, shielding users away from any unneeded mathematical and implementation details. @@ -36,7 +39,7 @@ arising in many modern inverse problems. Its API is designed to offer a class-ba to proximal operators, coupled with function-based optimizers; because of its modular design, researchers in the field of convex optimization can also benefit from this package in a number of ways when developing new algorithms: first, they can easily include their newly developed proximal operators and solvers; second, they can compare these methods -with state-of-the-art algorithms already provided in the package +with state-of-the-art algorithms already provided in the package. `PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], a Python package for matrix-free linear algebra and optimization. More specifically, `PyLops` is leveraged in the implementation of proximal operators that require @@ -58,15 +61,14 @@ Convex optimization is routinely used to solve problems of the form [@Parikh:201 \min_\mathbf{x} f(\mathbf{x}) +g(\mathbf{Lx}) \end{equation} -where $f$ and $g$ are possibly non-smooth convex functionals and $\mathbf{A}$ is a linear operator. A special case, -appearing in many scientific applications, is represented by $f=1/2 \Vert y - \mathcal{A}(\mathbf{x})\Vert_2^2$, which identifies -the so-called data misfit term. Here, $\mathcal{A}$ is a (possibly non-linear) modeling operator representing the underlying physical -process the links the unknown model vector $\mathbf{x}$ to the vector of observations $\mathbf{y}$. In this case, -we usually refer to $g$ as the regularization term, where one or multiple terms are added to the objective function to -promote certain features in the sought after solution and/or constraint the optimization process to produce a solution -within a given set of allowed vectors. +where $f$ and $g$ are possibly non-smooth convex functionals and $\mathbf{L}$ is a linear operator. A special case +appearing in many scientific applications is represented by $f=1/2 \Vert y - \mathcal{A}(\mathbf{x})\Vert_2^2$. +Here, $\mathcal{A}$ is a (possibly non-linear) modeling operator, describing the underlying physical +process that links the unknown model vector $\mathbf{x}$ to the vector of observations $\mathbf{y}$. In this case, +we usually refer to $g$ as the regularization term, where one or multiple terms are added to the data misfit term to +promote certain features in the sought after solution and/or constraint the solution to fall within a given set of allowed vectors. -Independent on the algorithm used to optimize such a cost function, a common feature of all proximal algorithms is +Independent on the algorithm used to optimize such an objective function, a common feature of all proximal algorithms is represented by the fact that one must be able to repeatedly evaluate the proximal operator of $f$ and/or $g$. The proximal operator of a function $f$ is defined as @@ -80,46 +82,47 @@ Whilst evaluating a proximal operator does itself require solving an optimizatio admit closed form solutions or can be solved very quickly with ad-hoc specialized methods. Several of such proximal operators are efficiently implemented in the ``PyProximal`` library. -Finally, there exists three main families of proximal algorithms that can be used to solve various flavors of equation +Finally, there exists three main families of proximal algorithms that can be used to solve various flavors of \autoref{eq:problem}, namely: - Proximal Gradient [@Combettes:2011]: this method, also commonly referred to as the Forward-Backward Splitting (FBS) algorithm, is usually the preferred choice when $\mathbf{L}=\mathbf{I}$ (i.e. identity operator). Accelerated versions such as the FISTA and TwIST algorithms exist and are usually preferred to the vanilla FBS method; -- Alternating Direction Method of Multipliers [@Boyd:2011]: this method is based on the well-known splitting strategy and can be used +- Alternating Direction Method of Multipliers [@Boyd:2011]: this method is based on a splitting strategy and can be used for a broader class of problem than FBS and its accelerated versions. -- Primal-Dual [@Chambolle:2011]: another popular algorithm able to tackle the generic problem in equation 1 with any choice of A. - It reformulates the original problem into its primal-dual version of solves a saddle optimization problem. +- Primal-Dual [@Chambolle:2011]: another popular algorithm able to tackle problems in the form of \autoref{eq:problem} with any choice of $\mathbf{L}$. + It reformulates the original problem into its primal-dual version and solves a saddle optimization problem. -``PyProximal`` provides implementations for these three families of algorithms; moreover, our solvers include additional features -such as back-tracking for automatic selection of step-sizes, logging of cost function evolution, and custom callbacks. +``PyProximal`` provides implementations for these three families of algorithms; moreover, all solvers include additional features +such as back-tracking for automatic selection of step-sizes, logging of the objective function evolution through iterations, +and possibility to inject custom callbacks. # Code structure -``PyProximal`` aims to provide a modular, and easy-to-use Application Programming Interface (API) that scientists -can use to define and solve convex objective functions by means of proximal algorithms. The API is composed of -two main units as shown in Fig. 1. +``PyProximal``'s modular and easy-to-use Application Programming Interface (API) allows scientists +to define and solve convex objective functions by means of proximal algorithms. The API is composed of +two main part as shown in Fig. 1. -The first unit contains the entire suite of proximal operators, which are class-based objects that subclass +The first part contains the entire suite of proximal operators, which are class-based objects subclassing the ``pylops.ProxOperator`` parent class. For each of these operators, the solution to the proximal optimization -problem in equation \autoref{eq:prox} (and/or the dual proximal problem) is implemented in the ``prox`` +problem in \autoref{eq:prox} (and/or the dual proximal problem) is implemented in the ``prox`` (and/or ``dualprox``) method. As in most cases a closed-form solution exists for such a problem, our -implementation provides users with the most efficient way to evaluate a proximal operator. The second unit comprises -of so-called proximal solvers, optimization algorithms that are suited to solve problems of the form in equation \autoref{eq:problem}. +implementation provides users with the most efficient way to evaluate a proximal operator. The second part comprises +of so-called proximal solvers, optimization algorithms that are suited to solve problems of the form in \autoref{eq:problem}. ![Schematic representation of the ``PyProximal`` API.](figs/software.png){ width=90% } # Representative PyProximal Use Cases -PyProximal has already been featured in a number of scientific publications: +Examples of PyProximal applications in different scientific fields include: -- Joint inversion and segmentation of subsurface models: when inverting geophysical data for subsurface priorities, - a prior information that we would like to include in the inversion process is represented by the presence of a - discrete number of rock units, which can be parametrized in terms of their expected mean (or most likely value). - Ravasi and Birnie (2022) framed such a problem as a joint inversion and segmentation where the underlying optimization - is solved in alternating fashion using the Primal-dual algorithm. -- Plug-and-Play (PnP) priors: introduced in 2013 by Vent, in the PnP framework any proximal operator is interpreted +- *Joint inversion and segmentation of subsurface models*: when inverting geophysical data for subsurface priorities, + prior information can be provided to inversion process in the form of discrete number of rock units; this can be + parametrized in terms of their expected mean (or most likely value). @Ravasi:2022 framed such a problem + as a joint inversion and segmentation where the underlying optimization is solved in alternating fashion using the + Primal-Dual algorithm. +- *Plug-and-Play (PnP) priors*: introduced in 2013 by Vent, in the PnP framework any proximal operator is interpreted as a denoising problem and solved by means of any statistical or deep learning based denoiser. Recently, Romero From e5259007cd7a9cceb1857fb3b97f1d7ec5d4672d Mon Sep 17 00:00:00 2001 From: mrava87 Date: Wed, 20 Dec 2023 09:43:32 +0300 Subject: [PATCH 17/23] Finalized first draft --- joss/paper.bib | 29 +++++++++++++++++++++++++++ joss/paper.md | 53 +++++++++++++++++++++++++++----------------------- 2 files changed, 58 insertions(+), 24 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index 0cc7bbe..4758ec1 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -53,4 +53,33 @@ @article{Ravasi:2022 volume = 228, doi = {10.1093/gji/ggab388}, url = {https://academic.oup.com/gji/article/228/2/893/6374557} +} + +@article{Venkatakrishnan:2013, + author = {S.V Venkatakrishnan and C.A. Bouman and B. Wohlberg}, + title = "{Plug-and-Play Priors for Model Based Reconstruction}", + journal = {2013 IEEE Global Conference on Signal and Information Processing}, + year = 2013, + doi = {10.1109/GlobalSIP.2013.6737048}, + url = {https://ieeexplore.ieee.org/document/6737048} +} + +@article{Romero:2023, + author = {J. Romero and N. Luiken and M. Ravasi}, + title = "{Seeing through the CO2 plume: Joint inversion-segmentation of the Sleipner 4D seismic data set}", + journal = {The Leading Edge}, + year = 2023, + volume = 42, + doi = {10.1190/tle42070457.1}, + url = {https://library.seg.org/doi/full/10.1190/tle42070457.1} +} + +@article{Romero:2022, + author = {J. Romero and M. Corrales N. Luiken and M. Ravasi}, + title = "{Plug and Play Post-Stack Seismic Inversion with CNN-Based Denoisers}", + journal = {Second EAGE Subsurface Intelligence Workshop}, + year = 2022, + volume = 1, + doi = {10.3997/2214-4609.2022616015}, + url = {https://www.earthdoc.org/content/papers/10.3997/2214-4609.2022616015} } \ No newline at end of file diff --git a/joss/paper.md b/joss/paper.md index 45cb7a0..fd25e2e 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -26,30 +26,30 @@ non-smooth and possibly constrained versions of such problems. These algorithms sit at a higher level of abstraction than gradient-based algorithms and require a basic operation to be performed at each iteration: the evaluation of the so-called proximal operator of the functional to be optimized. ``PyProximal`` is a Python-based library aimed at -democratizing the application of convex optimization to scientific problems, providing all the required +democratizing the application of convex optimization to scientific problems; it provides the required building blocks (i.e., proximal operators and algorithms) to define and solve complex, convex objective functions -in a high-level manner, shielding users away from any unneeded mathematical and implementation details. +in a high-level, abstract fashion, shielding users away from any unneeded mathematical and implementation details. # Statement of need -`PyProximal` is a Python package for convex optimization, developed as an integral part of the `PyLops` framework. +`PyProximal` is a Python library for convex optimization, developed as an integral part of the `PyLops` framework. It provides practitioners with an easy-to-use framework to define and solve composite convex objective functions arising in many modern inverse problems. Its API is designed to offer a class-based and user-friendly interface to proximal operators, coupled with function-based optimizers; because of its modular design, researchers in the field -of convex optimization can also benefit from this package in a number of ways when developing new algorithms: first, +of convex optimization can also benefit from this library in a number of ways when developing new algorithms: first, they can easily include their newly developed proximal operators and solvers; second, they can compare these methods -with state-of-the-art algorithms already provided in the package. +with state-of-the-art algorithms already provided in the library. -`PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], a Python package for matrix-free linear algebra +`PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], a Python library for matrix-free linear algebra and optimization. More specifically, `PyLops` is leveraged in the implementation of proximal operators that require access to linear operators (e.g., numerical derivatives) and/or least-squares solvers -(e.g., conjugate gradient). Whilst similar packages exist in the Python ecosystem, their design usually leads to a +(e.g., conjugate gradient). Whilst libraries with similar capabilities exist in the Python ecosystem, their design usually leads to a tight coupling between linear and proximal operators, and their respective solvers. On the other hand, by following the Separation of Concerns (SoC) design principle, the overlap between `PyLops` and `PyProximal` is reduced to a minimum, easing both their development and maintenance, as well as allowing newcomers to learn how to solve inverse problems in a step-by-step fashion. -As such, `PyProximal` can be ultimately described as a light-weight extension of `PyLops` that users of the former can very easily -learn and use with minimal additional effort. +As such, `PyProximal` can be ultimately described as a light-weight extension of `PyLops` that users of the latter can easily +learn and adopt with minimal additional effort. # Mathematical framework @@ -62,15 +62,14 @@ Convex optimization is routinely used to solve problems of the form [@Parikh:201 \end{equation} where $f$ and $g$ are possibly non-smooth convex functionals and $\mathbf{L}$ is a linear operator. A special case -appearing in many scientific applications is represented by $f=1/2 \Vert y - \mathcal{A}(\mathbf{x})\Vert_2^2$. +appearing in many scientific applications is represented by $f=1/2 \Vert \mathbf{y} - \mathcal{A}(\mathbf{x})\Vert_2^2$. Here, $\mathcal{A}$ is a (possibly non-linear) modeling operator, describing the underlying physical process that links the unknown model vector $\mathbf{x}$ to the vector of observations $\mathbf{y}$. In this case, -we usually refer to $g$ as the regularization term, where one or multiple terms are added to the data misfit term to +we usually refer to $g$ as the regularizer, where one or multiple functions are added to the data misfit term to promote certain features in the sought after solution and/or constraint the solution to fall within a given set of allowed vectors. -Independent on the algorithm used to optimize such an objective function, a common feature of all proximal algorithms is -represented by the fact that one must be able to repeatedly evaluate the proximal operator of $f$ and/or $g$. The proximal -operator of a function $f$ is defined as +A common feature of all proximal algorithms is represented by the fact that one must be able to repeatedly +evaluate the proximal operator of $f$ and/or $g$. The proximal operator of a function $f$ is defined as \begin{equation} \label{eq:prox} @@ -78,8 +77,8 @@ prox_{\tau f} (\mathbf{x}) = \min_{\mathbf{y}} f(\mathbf{y}) + \frac{1}{2 \tau}||\mathbf{y} - \mathbf{x}||^2_2 \end{equation} -Whilst evaluating a proximal operator does itself require solving an optimization problem, these subproblems often -admit closed form solutions or can be solved very quickly with ad-hoc specialized methods. Several of such proximal +Whilst evaluating a proximal operator does itself require solving an optimization problem, these problems often +admit closed form solutions or can be solved very efficiently with ad-hoc specialized methods. Several of such proximal operators are efficiently implemented in the ``PyProximal`` library. Finally, there exists three main families of proximal algorithms that can be used to solve various flavors of @@ -109,7 +108,8 @@ the ``pylops.ProxOperator`` parent class. For each of these operators, the solut problem in \autoref{eq:prox} (and/or the dual proximal problem) is implemented in the ``prox`` (and/or ``dualprox``) method. As in most cases a closed-form solution exists for such a problem, our implementation provides users with the most efficient way to evaluate a proximal operator. The second part comprises -of so-called proximal solvers, optimization algorithms that are suited to solve problems of the form in \autoref{eq:problem}. +of so-called proximal solvers, optimization algorithms that are suited to solve problems of the form in \autoref{eq:problem}. +Finally, some specialized solvers that rely on one or more of the previously described optimizers are also provided. ![Schematic representation of the ``PyProximal`` API.](figs/software.png){ width=90% } @@ -119,11 +119,16 @@ Examples of PyProximal applications in different scientific fields include: - *Joint inversion and segmentation of subsurface models*: when inverting geophysical data for subsurface priorities, prior information can be provided to inversion process in the form of discrete number of rock units; this can be - parametrized in terms of their expected mean (or most likely value). @Ravasi:2022 framed such a problem - as a joint inversion and segmentation where the underlying optimization is solved in alternating fashion using the - Primal-Dual algorithm. -- *Plug-and-Play (PnP) priors*: introduced in 2013 by Vent, in the PnP framework any proximal operator is interpreted - as a denoising problem and solved by means of any statistical or deep learning based denoiser. Recently, Romero - - + parametrized in terms of their expected mean (or most likely value). @Ravasi:2022 and @Romero:2023 frame such a problem + as a joint inversion and segmentation task, where the underlying objective function is optimized in alternating fashion + using the Primal-Dual algorithm. +- *Plug-and-Play (PnP) priors*: introduced in 2013 by @Venkatakrishnan:2013, the PnP framework lays its foundation on + the interpretation of the proximal operator as a denoising problem; as such, powerful statistical or deep learning + based denoisers are used to evaluate the proximal operator of implicit regularizers. @Romero:2022 applies this concept + in the context of seismic inversion, achieving results of superior quality in comparison to traditional model-based + regularization techniques. +- *EX3*: ... +- *EX4*: ... +- .... +- # References \ No newline at end of file From f597955d615fee06668ddeb463abed73ce280b60 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Wed, 20 Dec 2023 14:10:41 +0300 Subject: [PATCH 18/23] Added third app --- joss/paper.bib | 13 ++++++++++++- joss/paper.md | 5 ++++- 2 files changed, 16 insertions(+), 2 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index 4758ec1..f806aa1 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -82,4 +82,15 @@ @article{Romero:2022 volume = 1, doi = {10.3997/2214-4609.2022616015}, url = {https://www.earthdoc.org/content/papers/10.3997/2214-4609.2022616015} -} \ No newline at end of file +} + +@article{Leblanc:2023, + journal = {Second EAGE Subsurface Intelligence Workshop}, + year = 2023, + author = {O. Leblanc and M. Hofer and S. Sivankutty and H. Rigneault and L. Jacques}, + title = "{Interferometric Lensless Imaging: Rank-one Projections of Image Frequencies with Speckle Illuminations}", + url = {https://arxiv.org/abs/2306.12698}, + archivePrefix = {arXiv}, + journal = {ArXiv e-prints}, + +} diff --git a/joss/paper.md b/joss/paper.md index fd25e2e..098ecd5 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -127,7 +127,10 @@ Examples of PyProximal applications in different scientific fields include: based denoisers are used to evaluate the proximal operator of implicit regularizers. @Romero:2022 applies this concept in the context of seismic inversion, achieving results of superior quality in comparison to traditional model-based regularization techniques. -- *EX3*: ... +- *Multi-Core Fiber Lensless Imaging*: lensless imaging is a computational imaging technique to reconstruct biological + samples at cellular scale. Compressive sensing coupled with rank-one projections has been shown to improve the + efficiency of the acquisition process [@Leblanc:2023]; this entails solving a $L_1$ regularized inverse problem with + the proximal gradient method. - *EX4*: ... - .... - From 327327c0ca62b1b46744226304cbb3b03fb4e3e3 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Wed, 20 Dec 2023 16:01:14 +0300 Subject: [PATCH 19/23] Finalized third app --- joss/paper.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/joss/paper.md b/joss/paper.md index 098ecd5..afe2244 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -127,11 +127,11 @@ Examples of PyProximal applications in different scientific fields include: based denoisers are used to evaluate the proximal operator of implicit regularizers. @Romero:2022 applies this concept in the context of seismic inversion, achieving results of superior quality in comparison to traditional model-based regularization techniques. -- *Multi-Core Fiber Lensless Imaging*: lensless imaging is a computational imaging technique to reconstruct biological - samples at cellular scale. Compressive sensing coupled with rank-one projections has been shown to improve the - efficiency of the acquisition process [@Leblanc:2023]; this entails solving a $L_1$ regularized inverse problem with - the proximal gradient method. +- *Multi-Core Fiber Lensless Imaging* (MCFLI) is a computational imaging technique to reconstruct biological + samples at cellular scale. Leveraging the rank-one projected interferometric sensing of the MCFLI has been shown to + improve the efficiency of the acquisition process [@Leblanc:2023]; this entails solving a regularized inverse problem with + the proximal gradient method. Depending on the image to be reconstructed, the regularization term may for instance be $L_1$ or TV. - *EX4*: ... - .... -- + # References \ No newline at end of file From 6b95d64c1a5641fc0200bb164fe47918f950a9c2 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Wed, 20 Dec 2023 16:11:27 +0300 Subject: [PATCH 20/23] Add more authors --- joss/paper.md | 17 ++++++++++++++--- 1 file changed, 14 insertions(+), 3 deletions(-) diff --git a/joss/paper.md b/joss/paper.md index afe2244..6c94fb4 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -7,15 +7,26 @@ tags: authors: - name: Matteo Ravasi orcid: 0000-0003-0020-2721 - corresponding: true # (This is how to denote the corresponding author) + corresponding: true affiliation: 1 # (Multiple affiliations must be quoted) + - name: Olivier Leblanc + orcid: 0000-0003-3641-1875 + affiliation: 2 + - name: Marcus Valtonen Ornhag + orcid: 0000-0001-8687-227X + affiliation: 3 affiliations: - - name: Earth Science and Engineering, Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Kingdom of Saudi Arabia - index: 1 + - name: Earth Science and Engineering, Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Kingdom of Saudi Arabia + index: 1 + - name: ISPGroup, INMA/ICTEAM, UCLouvain, Louvain-la-Neuve, Belgium. + index: 2 + - name: Ericsson, Lund, Sweden. + index: 3 date: 19 December 2023 bibliography: paper.bib --- + # Summary A broad class of problems in scientific disciplines ranging from image processing and astrophysics, From 850069c0bad4d05e80ed79bbe08689c7e2085f99 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Thu, 21 Dec 2023 21:06:18 +0300 Subject: [PATCH 21/23] Added eurunuela to authors --- joss/paper.md | 17 ++++++++++------- 1 file changed, 10 insertions(+), 7 deletions(-) diff --git a/joss/paper.md b/joss/paper.md index 6c94fb4..9369bac 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -9,19 +9,24 @@ authors: orcid: 0000-0003-0020-2721 corresponding: true affiliation: 1 # (Multiple affiliations must be quoted) - - name: Olivier Leblanc - orcid: 0000-0003-3641-1875 - affiliation: 2 - name: Marcus Valtonen Ornhag orcid: 0000-0001-8687-227X + affiliation: 2 + - name: Olivier Leblanc + orcid: 0000-0003-3641-1875 affiliation: 3 + - name: Eneko Urunuela + orcid: 0000-0001-6849-9088 + affiliation: 4 affiliations: - name: Earth Science and Engineering, Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Kingdom of Saudi Arabia index: 1 - - name: ISPGroup, INMA/ICTEAM, UCLouvain, Louvain-la-Neuve, Belgium. - index: 2 - name: Ericsson, Lund, Sweden. + index: 2 + - name: ISPGroup, INMA/ICTEAM, UCLouvain, Louvain-la-Neuve, Belgium. index: 3 + - name: Basque Center on Cognition, Brain and Language (BCBL), Donostia-San Sebastián, Spain. + index: 4 date: 19 December 2023 bibliography: paper.bib --- @@ -142,7 +147,5 @@ Examples of PyProximal applications in different scientific fields include: samples at cellular scale. Leveraging the rank-one projected interferometric sensing of the MCFLI has been shown to improve the efficiency of the acquisition process [@Leblanc:2023]; this entails solving a regularized inverse problem with the proximal gradient method. Depending on the image to be reconstructed, the regularization term may for instance be $L_1$ or TV. -- *EX4*: ... -- .... # References \ No newline at end of file From 102264d7e05484a7428017fa89126587da43442d Mon Sep 17 00:00:00 2001 From: mrava87 Date: Sun, 31 Dec 2023 14:39:33 +0300 Subject: [PATCH 22/23] Added Nick Luiken to authors --- joss/paper.md | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/joss/paper.md b/joss/paper.md index 9369bac..b55060d 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -8,10 +8,13 @@ authors: - name: Matteo Ravasi orcid: 0000-0003-0020-2721 corresponding: true - affiliation: 1 # (Multiple affiliations must be quoted) + affiliation: 1 - name: Marcus Valtonen Ornhag orcid: 0000-0001-8687-227X affiliation: 2 + - name: Nick Luiken + orcid: 0000-0003-3307-1748 + affiliation: 1 - name: Olivier Leblanc orcid: 0000-0003-3641-1875 affiliation: 3 From 4bbd10b99da485231fd8d3e4de176c8dbc516b44 Mon Sep 17 00:00:00 2001 From: mrava87 Date: Sun, 31 Dec 2023 14:48:35 +0300 Subject: [PATCH 23/23] Added mention to scalability --- joss/paper.bib | 11 +++++++++++ joss/paper.md | 3 ++- 2 files changed, 13 insertions(+), 1 deletion(-) diff --git a/joss/paper.bib b/joss/paper.bib index f806aa1..f1c6613 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -94,3 +94,14 @@ @article{Leblanc:2023 journal = {ArXiv e-prints}, } + + +@article{Ravasi:2021, + author = {M. Ravasi}, + title = "{Leveraging GPUs for matrix-free optimization with PyLops}", + journal = {Fifth EAGE Workshop on High Performance Computing for Upstream}, + year = 2021, + volume = 1, + doi = {10.3997/2214-4609.2021612003}, + url = {https://www.earthdoc.org/content/papers/10.3997/2214-4609.2021612003} +} \ No newline at end of file diff --git a/joss/paper.md b/joss/paper.md index b55060d..c011746 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -61,7 +61,8 @@ they can easily include their newly developed proximal operators and solvers; se with state-of-the-art algorithms already provided in the library. `PyProximal` heavily relies on and seamlessly integrates with `PyLops` [@Ravasi:2020], a Python library for matrix-free linear algebra -and optimization. More specifically, `PyLops` is leveraged in the implementation of proximal operators that require +and optimization. As such, it can seamlessy handle problems with millions of unknowns and inherits +the interchangle CPU/GPU backend of PyLops [@Ravasi:2021]. More specifically, `PyLops` is leveraged in the implementation of proximal operators that require access to linear operators (e.g., numerical derivatives) and/or least-squares solvers (e.g., conjugate gradient). Whilst libraries with similar capabilities exist in the Python ecosystem, their design usually leads to a tight coupling between linear and proximal operators, and their respective solvers. On the other hand, by following the