Linear Inverse Problems Using a Generative Compound Gaussian Prior

TL;DR

This paper introduces a novel iterative algorithm that combines a GAN prior with a compound Gaussian distribution to improve solutions of ill-posed inverse imaging problems, demonstrating superior performance and generalizability.

Contribution

The paper develops a new algorithm integrating GAN and compound Gaussian priors for inverse problems, with proven convergence and empirical validation.

Findings

Outperforms existing methods in compressive sensing and tomography.

Provides improved generalizability over prior GAN-based approaches.

Avoids performance saturation issues in previous methods.

Abstract

Since most inverse problems arising in scientific and engineering applications are ill-posed, prior information about the solution space is incorporated, typically through regularization, to establish a well-posed problem with a unique solution. Often, this prior information is an assumed statistical distribution of the desired inverse problem solution. Recently, due to the unprecedented success of generative adversarial networks (GANs), the generative network from a GAN has been implemented as the prior information in imaging inverse problems. In this paper, we devise a novel iterative algorithm to solve inverse problems in imaging where a dual-structured prior is imposed by combining a GAN prior with the compound Gaussian (CG) class of distributions. A rigorous computational theory for the convergence of the proposed iterative algorithm, which is based upon the alternating direction method of multipliers, is established. Furthermore, elaborate empirical results for the proposed iterative algorithm are presented. By jointly exploiting the powerful CG and GAN classes of image priors, we find, in compressive sensing and tomographic imaging problems, our proposed algorithm outperforms and provides improved generalizability over competitive prior art approaches while avoiding performance saturation issues in previous GAN prior-based methods.