Amortised MAP Inference for Image Super-resolution
Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often with a pixel-wise mean squared error (MSE) loss. However, the outputs from such methods tend to be blurry, over-smoothed and generally appear implausible. A more desirable approach would employ Maximum a Posteriori (MAP) inference, preferring solutions that always have a high probability under the image prior, and thus appear more plausible. Direct MAP estimation for SR is non-trivial, as it requires us to build a model for the image prior from samples. Here we introduce new methods for emph{amortised MAP inference} whereby we calculate the MAP estimate directly using a convolutional neural network. We first introduce a novel neural network architecture that performs a projection to the affine subspace of valid SR solutions ensuring that the high resolution output of the network is always consistent with the low resolution input. We show that, using this architecture, the amortised MAP inference problem reduces to minimising the cross-entropy between two distributions, similar to training generative models. We propose three methods to solve this optimisation problem: (1) Generative Adversarial Networks (GAN) (2) denoiser-guided SR which backpropagates gradient-estimates from denoising to train the network, and (3) a baseline method using a maximum-likelihood-trained image prior. Our experiments show that the GAN based approach performs best on real image data. Lastly, we establish a connection between GANs and amortised variational inference as in e.g. variational autoencoders.
The paper presents an amortised MAP estimation method for SR problems. By learning a neural network which learns to project to an affine subspace of SR solutions which are consistent with the LR method the method enables finding propoer solutions with by using a variety of methods: GANs, noise assisted and density assisted optimisation. Results are nicely demonstrated on several datasets. I like the paper all in all, though I feel the writing can be polished by quite a bit and presentation should be made clearer. It was hard to follow at times and considering the subject matter is quite complicated making it clearer would help. Also, I would love to see some more analysis of the resulting the networks - what kind of features to they learn?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Amortised MAP Inference for Image Super-resolution
Image super-resolution (SR) is an underdetermined inverse problem, where a large number of plausible high resolution images can explain the same downsampled image. Most current single image SR methods use empirical risk minimisation, often with a pixel-wise mean squared error (MSE) loss. However, the outputs from such methods tend to be blurry, over-smoothed and generally appear implausible. A more desirable approach would employ Maximum a Posteriori (MAP) inference, preferring solutions that always have a high probability under the image prior, and thus appear more plausible. Direct MAP estimation for SR is non-trivial, as it requires us to build a model for the image prior from samples. Here we introduce new methods for emph{amortised MAP inference} whereby we calculate the MAP estimate directly using a convolutional neural network. We first introduce a novel neural network architecture that performs a projection to the affine subspace of valid SR solutions ensuring that the high resolution output of the network is always consistent with the low resolution input. We show that, using this architecture, the amortised MAP inference problem reduces to minimising the cross-entropy between two distributions, similar to training generative models. We propose three methods to solve this optimisation problem: (1) Generative Adversarial Networks (GAN) (2) denoiser-guided SR which backpropagates gradient-estimates from denoising to train the network, and (3) a baseline method using a maximum-likelihood-trained image prior. Our experiments show that the GAN based approach performs best on real image data. Lastly, we establish a connection between GANs and amortised variational inference as in e.g. variational autoencoders.
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>



The paper presents an amortised MAP estimation method for SR problems. By learning a neural network which learns to project to an affine subspace of SR solutions which are consistent with the LR method the method enables finding propoer solutions with by using a variety of methods: GANs, noise assisted and density assisted optimisation. Results are nicely demonstrated on several datasets. I like the paper all in all, though I feel the writing can be polished by quite a bit and presentation should be made clearer. It was hard to follow at times and considering the subject matter is quite complicated making it clearer would help. Also, I would love to see some more analysis of the resulting the networks - what kind of features to they learn?
assistant
The paper presents an amortised MAP estimation method for SR problems. By learning a neural network which learns to project to an affine subspace of SR solutions which are consistent with the LR method the method enables finding propoer solutions with by using a variety of methods: GANs, noise assisted and density assisted optimisation. Results are nicely demonstrated on several datasets. I like the paper all in all, though I feel the writing can be polished by quite a bit and presentation should be made clearer. It was hard to follow at times and considering the subject matter is quite complicated making it clearer would help. Also, I would love to see some more analysis of the resulting the networks - what kind of features to they learn?