  While deep learning methods have achieved state-of-the-art performance in
many challenging inverse problems like image inpainting and super-resolution,
they invariably involve problem-specific training of the networks. Under this
approach, different problems require different networks. In scenarios where we
need to solve a wide variety of problems, e.g., on a mobile camera, it is
inefficient and costly to use these specially-trained networks. On the other
hand, traditional methods using signal priors can be used in all linear inverse
problems but often have worse performance on challenging tasks. In this work,
we provide a middle ground between the two kinds of methods --- we propose a
general framework to train a single deep neural network that solves arbitrary
linear inverse problems. The proposed network acts as a proximal operator for
an optimization algorithm and projects non-image signals onto the set of
natural images defined by the decision boundary of a classifier. In our
experiments, the proposed framework demonstrates superior performance over
traditional methods using a wavelet sparsity prior and achieves comparable
performance of specially-trained networks on tasks including compressive
sensing and pixel-wise inpainting.
