Total Variation Superiorized Conjugate Gradient Method for Image Reconstruction

TL;DR

This paper introduces a novel superiorized conjugate gradient method incorporating total variation regularization for image reconstruction, demonstrating improved image quality and computational efficiency over existing methods like FISTA.

Contribution

It proposes five variants of superiorized conjugate gradient methods with TV regularization, showing they can outperform FISTA in image reconstruction quality and speed.

Findings

Superiorized CG variants produce higher quality images.

Some variants outperform FISTA in reconstruction quality.

Proposed methods are faster than traditional non-linear CG approaches.

Abstract

The conjugate gradient (CG) method is commonly used for the rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization should be utilized. Total variation (TV) is a useful regularization penalty, frequently utilized in image reconstruction for generating images with sharp edges. When a non-quadratic norm is selected for regularization, as is the case for TV, then it is no longer possible to use CG. Non-linear CG is an alternative, but it does not share the efficiency that CG shows with least squares and methods such as fast iterative shrinkage-thresholding algorithms (FISTA) are preferred for problems with TV norm. A different approach to including prior information is superiorization. In this paper it is shown that the conjugate gradient method can be superiorized. Five different CG variants are proposed, including preconditioned CG. The CG methods superiorized by the total variation norm are presented and their performance in image reconstruction is demonstrated. It is illustrated that some of the proposed variants of the superiorized CG method can produce reconstructions of superior quality to those produced by FISTA and in less computational time, due to the speed of the original CG for least squares problems.