Regularising Inverse Problems with Generative Machine Learning Models

TL;DR

This paper explores the use of generative models as regularisers in inverse imaging problems, evaluating their effectiveness and proposing criteria to assess model quality, with experiments on deblurring, deconvolution, and tomography.

Contribution

It introduces the concept of generative regularisers, proposes criteria to evaluate generative models, and compares different models and regularisers on various inverse problems.

Findings

Allowing small deviations from the generator's range improves results.

Generative regularisers can produce good inverse problem solutions.

Evaluation criteria help guide future generative model development.

Abstract

Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family \textit{generative regularisers}. The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that restricting solutions of the inverse problem to lie exactly in the range of a generative model can give good results but that allowing small deviations from the range of the generator produces more consistent results.