Equivariance Regularization for Image Reconstruction

TL;DR

This paper introduces Regularization-by-Equivariance (REV), a novel regularization method leveraging physical symmetries in inverse imaging problems, improving reconstruction quality in sparse-view X-ray CT tasks.

Contribution

The paper presents REV, a structure-adaptive regularization scheme that exploits measurement equivariance, compatible with existing optimization algorithms for improved inverse problem solutions.

Findings

Effective in sparse-view X-ray CT reconstruction

Plug-and-play compatibility with optimization algorithms

Mitigates ill-posedness of inverse problems

Abstract

In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant structure in the physics of the measurements -- which is prevalent in many inverse problems such as tomographic image reconstruction -- to mitigate the ill-poseness of the inverse problem. Our proposed scheme can be applied in a plug-and-play manner alongside with any classic first-order optimization algorithm such as the accelerated gradient descent/FISTA for simplicity and fast convergence. The numerical experiments in sparse-view X-ray CT image reconstruction tasks demonstrate the effectiveness of our approach.