OPTIMAL TRANSPORT, CYCLEGAN, AND PENALIZED LS FOR UNSUPERVISED LEARNING IN INVERSE PROBLEMS
The penalized least squares (PLS) is a classic approach to inverse problems, where a regularization term is added to stabilize the solution. Optimal transport (OT) is another mathematical framework for computer vision tasks by providing means to transport one measure to another at minimal cost. Cycle-consistent generative adversarial network (cycleGAN) is a recent extension of GAN to learn target distributions with less mode collapsing behavior. Although similar in that no supervised training is required, the algorithms look different, so the mathematical relationship between these approaches is not clear. In this article, we provide an important advance to unveil the missing link. Specifically, we reveal that a cycleGAN architecture can be derived as a dual formulation of the optimal transport problem, if the PLS with a deep learning penalty is used as a transport cost between the two probability measures from measurements and unknown images. This suggests that cycleGAN can be considered as stochastic generalization of classical PLS approaches. Our derivation is so general that various types of cycleGAN architecture can be easily derived by merely changing the transport cost. As proofs of concept, this paper provides novel cycleGAN architecture for unsupervised learning in accelerated MRI and deconvolution microscopy problems, which confirm the efficacy and the flexibility of the theory.
This paper frames and contextualizes CycleGAN as a stochastic generalization of penalized least squares for inverse problems, providing several unifying theorems, rederiving some modern CycleGAN architectures within the optimal transport framework, and also demonstrating the practical use of modified architectures derived using this framework for accelerated MRI and microscopy. While I did not check the proofs in detail, the additional generalization of a well-known, working architecture and additional variants used practically seem significant to me. Demonstrating the deep relationships in the proofs and propositions shown here, followed by two clear and concise derivations *and their practical application* is compelling, making this paper broadly applicable to both practitioners of compressed sensing and generative modeling. Frankly, it will take me some time to digest the proofs and overall relationships shown in the Propositions here, as I am not deeply familiar with optimal transport. The applied sections are direct, with Figure 5 being especially meaningful. There are a few small grammatical issues in the text - a careful re-read and edit with particular focus on grammar and style would be beneficial, though as it stands these small flaws didn*t meaningfully detract from the paper. The primary thing the authors could do in order to raise my score, would be to take an additional pass at grammatical clarity for the paper. More experiments are always beneficial, and I would encourage the authors to release source code to replicate some form of their experiments if possible. Some additional references which may be useful additions, primarily for interested readers to gain further background on the use of deep models for compressed sensing: Compressed Sensing with Deep Image Prior and Learned Regularization https://arxiv.org/abs/1806.06438 Compressed Sensing using Generative Models https://arxiv.org/abs/1703.03208 Deep Compressed Sensing http://proceedings.mlr.press/v97/wu19d/wu19d.pdf
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
OPTIMAL TRANSPORT, CYCLEGAN, AND PENALIZED LS FOR UNSUPERVISED LEARNING IN INVERSE PROBLEMS
The penalized least squares (PLS) is a classic approach to inverse problems, where a regularization term is added to stabilize the solution. Optimal transport (OT) is another mathematical framework for computer vision tasks by providing means to transport one measure to another at minimal cost. Cycle-consistent generative adversarial network (cycleGAN) is a recent extension of GAN to learn target distributions with less mode collapsing behavior. Although similar in that no supervised training is required, the algorithms look different, so the mathematical relationship between these approaches is not clear. In this article, we provide an important advance to unveil the missing link. Specifically, we reveal that a cycleGAN architecture can be derived as a dual formulation of the optimal transport problem, if the PLS with a deep learning penalty is used as a transport cost between the two probability measures from measurements and unknown images. This suggests that cycleGAN can be considered as stochastic generalization of classical PLS approaches. Our derivation is so general that various types of cycleGAN architecture can be easily derived by merely changing the transport cost. As proofs of concept, this paper provides novel cycleGAN architecture for unsupervised learning in accelerated MRI and deconvolution microscopy problems, which confirm the efficacy and the flexibility of the theory.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper frames and contextualizes CycleGAN as a stochastic generalization of penalized least squares for inverse problems, providing several unifying theorems, rederiving some modern CycleGAN architectures within the optimal transport framework, and also demonstrating the practical use of modified architectures derived using this framework for accelerated MRI and microscopy. While I did not check the proofs in detail, the additional generalization of a well-known, working architecture and additional variants used practically seem significant to me. Demonstrating the deep relationships in the proofs and propositions shown here, followed by two clear and concise derivations *and their practical application* is compelling, making this paper broadly applicable to both practitioners of compressed sensing and generative modeling. Frankly, it will take me some time to digest the proofs and overall relationships shown in the Propositions here, as I am not deeply familiar with optimal transport. The applied sections are direct, with Figure 5 being especially meaningful. There are a few small grammatical issues in the text - a careful re-read and edit with particular focus on grammar and style would be beneficial, though as it stands these small flaws didn*t meaningfully detract from the paper. The primary thing the authors could do in order to raise my score, would be to take an additional pass at grammatical clarity for the paper. More experiments are always beneficial, and I would encourage the authors to release source code to replicate some form of their experiments if possible. Some additional references which may be useful additions, primarily for interested readers to gain further background on the use of deep models for compressed sensing: Compressed Sensing with Deep Image Prior and Learned Regularization https://arxiv.org/abs/1806.06438 Compressed Sensing using Generative Models https://arxiv.org/abs/1703.03208 Deep Compressed Sensing http://proceedings.mlr.press/v97/wu19d/wu19d.pdf
assistant
This paper frames and contextualizes CycleGAN as a stochastic generalization of penalized least squares for inverse problems, providing several unifying theorems, rederiving some modern CycleGAN architectures within the optimal transport framework, and also demonstrating the practical use of modified architectures derived using this framework for accelerated MRI and microscopy. While I did not check the proofs in detail, the additional generalization of a well-known, working architecture and additional variants used practically seem significant to me. Demonstrating the deep relationships in the proofs and propositions shown here, followed by two clear and concise derivations *and their practical application* is compelling, making this paper broadly applicable to both practitioners of compressed sensing and generative modeling. Frankly, it will take me some time to digest the proofs and overall relationships shown in the Propositions here, as I am not deeply familiar with optimal transport. The applied sections are direct, with Figure 5 being especially meaningful. There are a few small grammatical issues in the text - a careful re-read and edit with particular focus on grammar and style would be beneficial, though as it stands these small flaws didn*t meaningfully detract from the paper. The primary thing the authors could do in order to raise my score, would be to take an additional pass at grammatical clarity for the paper. More experiments are always beneficial, and I would encourage the authors to release source code to replicate some form of their experiments if possible. Some additional references which may be useful additions, primarily for interested readers to gain further background on the use of deep models for compressed sensing: Compressed Sensing with Deep Image Prior and Learned Regularization https://arxiv.org/abs/1806.06438 Compressed Sensing using Generative Models https://arxiv.org/abs/1703.03208 Deep Compressed Sensing http://proceedings.mlr.press/v97/wu19d/wu19d.pdf