Invertible generative models for inverse problems: mitigating representation error and dataset bias
Trained generative models have shown remarkable performance as priors for inverse problems in imaging. For example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Our formulation is an empirical risk minimization that does not directly optimize the likelihood of images, as one would expect. Instead we optimize the likelihood of the latent representation of images as a proxy, as this is empirically easier. For compressive sensing, our formulation can yield higher accuracy than sparsity priors across almost all undersampling ratios. For the same accuracy on test images, they can use 10-20x fewer measurements. We demonstrate that invertible priors can yield better reconstructions than sparsity priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images.
This paper investigates the performance of invertible generative models for solving inverse problems. They argue that their most significant benefit over GAN priors is the lack of representation error that (1) enables invertible models to perform well on out-of-distribution data and (2) results in a model that does not saturate with increased number of measurements (as observed with GANs). They use a pre-trained Glow invertible network for the generator and solve a proxy for the maximum likelihood formulation of the problem, where the likelihood of an image is replaced by the likelihood of its latent representation. They demonstrate results on problems such as denoising, inpainting and compressed sensing. In all these applications, the invertible network consistently outperforms DCGAN across all noise levels/number of measurements. Furthermore, they demonstrate visually reasonable results on natural images significantly different from those in the training dataset. The idea of using invertible networks for estimating a specific forward process is not new, as the authors also pointed out. The contribution of this paper is that they use a pre-trained invertible model as a prior in various tasks not known in training time and support their technique with experimental results and therefore I would recommend accepting this paper. Since one of the main arguments in the paper is how the lack of representation error benefits the Glow prior compared to DCGAN prior, it would be interesting to see the representation error quantitatively for the DCGAN results and how it contributes to the total error. Moreover, demonstrating the comparison results in other metrics than PSNR (MSE, SSIM) would be interesting and more comprehensive.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Invertible generative models for inverse problems: mitigating representation error and dataset bias
Trained generative models have shown remarkable performance as priors for inverse problems in imaging. For example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Our formulation is an empirical risk minimization that does not directly optimize the likelihood of images, as one would expect. Instead we optimize the likelihood of the latent representation of images as a proxy, as this is empirically easier. For compressive sensing, our formulation can yield higher accuracy than sparsity priors across almost all undersampling ratios. For the same accuracy on test images, they can use 10-20x fewer measurements. We demonstrate that invertible priors can yield better reconstructions than sparsity priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images.
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 investigates the performance of invertible generative models for solving inverse problems. They argue that their most significant benefit over GAN priors is the lack of representation error that (1) enables invertible models to perform well on out-of-distribution data and (2) results in a model that does not saturate with increased number of measurements (as observed with GANs). They use a pre-trained Glow invertible network for the generator and solve a proxy for the maximum likelihood formulation of the problem, where the likelihood of an image is replaced by the likelihood of its latent representation. They demonstrate results on problems such as denoising, inpainting and compressed sensing. In all these applications, the invertible network consistently outperforms DCGAN across all noise levels/number of measurements. Furthermore, they demonstrate visually reasonable results on natural images significantly different from those in the training dataset. The idea of using invertible networks for estimating a specific forward process is not new, as the authors also pointed out. The contribution of this paper is that they use a pre-trained invertible model as a prior in various tasks not known in training time and support their technique with experimental results and therefore I would recommend accepting this paper. Since one of the main arguments in the paper is how the lack of representation error benefits the Glow prior compared to DCGAN prior, it would be interesting to see the representation error quantitatively for the DCGAN results and how it contributes to the total error. Moreover, demonstrating the comparison results in other metrics than PSNR (MSE, SSIM) would be interesting and more comprehensive.
assistant
This paper investigates the performance of invertible generative models for solving inverse problems. They argue that their most significant benefit over GAN priors is the lack of representation error that (1) enables invertible models to perform well on out-of-distribution data and (2) results in a model that does not saturate with increased number of measurements (as observed with GANs). They use a pre-trained Glow invertible network for the generator and solve a proxy for the maximum likelihood formulation of the problem, where the likelihood of an image is replaced by the likelihood of its latent representation. They demonstrate results on problems such as denoising, inpainting and compressed sensing. In all these applications, the invertible network consistently outperforms DCGAN across all noise levels/number of measurements. Furthermore, they demonstrate visually reasonable results on natural images significantly different from those in the training dataset. The idea of using invertible networks for estimating a specific forward process is not new, as the authors also pointed out. The contribution of this paper is that they use a pre-trained invertible model as a prior in various tasks not known in training time and support their technique with experimental results and therefore I would recommend accepting this paper. Since one of the main arguments in the paper is how the lack of representation error benefits the Glow prior compared to DCGAN prior, it would be interesting to see the representation error quantitatively for the DCGAN results and how it contributes to the total error. Moreover, demonstrating the comparison results in other metrics than PSNR (MSE, SSIM) would be interesting and more comprehensive.