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

J. H. Rick Chang, Chun-Liang Li, Barnabas Poczos, B. V. K. Vijaya Kumar, Aswin C. Sankaranarayanan; Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2017, pp. 5888-5897

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, each inverse problem requires its own dedicated network. In scenarios where we need to solve a wide variety of problems, e.g., on a mobile camera, it is inefficient and expensive to use these problem-specific networks. On the other hand, traditional methods using analytic signal priors can be used to solve any linear inverse problem; this often comes with a performance that is worse than learning-based methods. 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. We achieve this by training a network that acts as a quasi-projection operator for the set of natural images and show that any linear inverse problem involving natural images can be solved using iterative methods. We empirically show that the proposed framework demonstrates superior performance over traditional methods using wavelet sparsity prior while achieving performance comparable to specially-trained networks on tasks including compressive sensing and pixel-wise inpainting.