Deep neural networks have been very successful in compressive-sensing and image restoration applications, as a means to estimate images from partial, blurry, or otherwise degraded measurements. These networks are trained on a large number of corresponding pairs of measurements and ground-truth images, and thus implicitly learn to exploit domain-specific image statistics. But unlike measurement data, it is often expensive or impractical to collect a large training set of ground-truth images in many application settings. In this paper, we introduce an unsupervised framework for training image estimation networks, from a training set that contains only measurements---with two varied measurements per image---but no ground-truth for the full images desired as output. We demonstrate that our framework can be applied for both regular and blind image estimation tasks, where in the latter case parameters of the measurement model (e.g., the blur kernel) are unknown: during inference, and potentially, also during training. We evaluate our framework for training networks for compressive-sensing and blind deconvolution, considering both non-blind and blind training for the latter. Our framework yields models that are nearly as accurate as those from fully supervised training, despite not having access to any ground-truth images.

Originality: The paper is mainly based on the idea presented in [14] and could be considered a generalization of it. Section 3.2 is the part which makes this paper's originality clear. Quality: Quality is the issue which makes the reviewer to believe this paper is not ready for publication yet. Here are the issues: - First of all, there are few previous works on the exact same problem that are neither cited nor compared against in this manuscript. These papers even do not need either ground truth data or two sets of measurements (unlike the submitted paper) and have shown impressive results.

This work introduces a new method to learn image restoration methods from only corrupted data sets. It is an exciting idea that could potentially open up new applications for deep learning methods in settings where it is not possible to obtain ground truth data. Three reviewers initially assessed the work as 5/9/6. Based on a strong author rebuttal all reviewers took part in a discussion and two reviewers revised their score upwards, for a final assessment of 6/9/7. Overall this paper contains an exciting idea and is likely to stimulate the NeurIPS community to further consider the setting of learning only from corrupted data.

Deep neural networks have been very successful in compressive-sensing and image restoration applications, as a means to estimate images from partial, blurry, or otherwise degraded measurements. These networks are trained on a large number of corresponding pairs of measurements and ground-truth images, and thus implicitly learn to exploit domain-specific image statistics. But unlike measurement data, it is often expensive or impractical to collect a large training set of ground-truth images in many application settings. In this paper, we introduce an unsupervised framework for training image estimation networks, from a training set that contains only measurements---with two varied measurements per image---but no ground-truth for the full images desired as output. We demonstrate that our framework can be applied for both regular and blind image estimation tasks, where in the latter case parameters of the measurement model (e.g., the blur kernel) are unknown: during inference, and potentially, also during training. We evaluate our framework for training networks for compressive-sensing and blind deconvolution, considering both non-blind and blind training for the latter.

Deep neural networks have been very successful in compressive-sensing and image restoration applications, as a means to estimate images from partial, blurry, or otherwise degraded measurements. These networks are trained on a large number of corresponding pairs of measurements and ground-truth images, and thus implicitly learn to exploit domain-specific image statistics. But unlike measurement data, it is often expensive or impractical to collect a large training set of ground-truth images in many application settings. In this paper, we introduce an unsupervised framework for training image estimation networks, from a training set that contains only measurements---with two varied measurements per image---but no ground-truth for the full images desired as output. We demonstrate that our framework can be applied for both regular and blind image estimation tasks, where in the latter case parameters of the measurement model (e.g., the blur kernel) are unknown: during inference, and potentially, also during training.