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While deep learning methods have achieved state-of-the-art performance inmany challenging inverse problems like image inpainting and super-resolution,they invariably involve problem-specific training of the networks. Under thisapproach, different problems require different networks. In scenarios where weneed to solve a wide variety of problems, e.g., on a mobile camera, it isinefficient and costly to use these specially-trained networks. On the otherhand, traditional methods using signal priors can be used in all linear inverseproblems but often have worse performance on challenging tasks. In this work,we provide a middle ground between the two kinds of methods --- we propose ageneral framework to train a single deep neural network that solves arbitrarylinear inverse problems. The proposed network acts as a proximal operator foran optimization algorithm and projects non-image signals onto the set ofnatural images defined by the decision boundary of a classifier. In ourexperiments, the proposed framework demonstrates superior performance overtraditional methods using a wavelet sparsity prior and achieves comparableperformance of specially-trained networks on tasks including compressivesensing and pixel-wise inpainting.

One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models