One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models
This provides a general solution for mobile and embedded systems needing to handle various inverse problems without training separate networks, though it is incremental in bridging deep learning and traditional optimization methods.
The authors tackled the inefficiency of problem-specific deep learning models for linear inverse problems by proposing a single neural network framework that acts as a proximal operator, achieving superior performance over traditional wavelet-based methods and comparable results to specialized networks in tasks like compressive sensing and pixel-wise inpainting.
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.