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

TL;DR

This paper introduces a universal deep neural network framework that can solve various linear inverse problems efficiently, outperforming traditional methods and matching specialized networks in performance.

Contribution

The authors propose a single, general deep network acting as a proximal operator to solve multiple linear inverse problems without problem-specific training.

Findings

Outperforms traditional wavelet sparsity methods.

Achieves comparable results to specialized networks on key tasks.

Demonstrates versatility across diverse inverse problems.

Abstract

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.