DRIP: Deep Regularizers for Inverse Problems

TL;DR

This paper introduces a new family of neural regularizers based on variational principles that guarantee data fidelity in solving highly ill-posed inverse problems like image deblurring and tomography.

Contribution

It proposes neural regularizers grounded in variational formulations that ensure solutions fit the data, addressing limitations of previous deep learning approaches.

Findings

Regularizers guarantee data fitting in inverse problems

Effective on image deblurring and tomography tasks

Outperforms existing methods in ill-posed scenarios

Abstract

In this paper we consider inverse problems that are mathematically ill-posed. That is, given some (noisy) data, there is more than one solution that approximately fits the data. In recent years, deep neural techniques that find the most appropriate solution, in the sense that it contains a-priori information, were developed. However, they suffer from several shortcomings. First, most techniques cannot guarantee that the solution fits the data at inference. Second, while the derivation of the techniques is inspired by the existence of a valid scalar regularization function, such techniques do not in practice rely on such a function, and therefore veer away from classical variational techniques. In this work we introduce a new family of neural regularizers for the solution of inverse problems. These regularizers are based on a variational formulation and are guaranteed to fit the data. We demonstrate their use on a number of highly ill-posed problems, from image deblurring to limited angle tomography.