First-order convex feasibility algorithms for iterative image reconstruction in X-ray CT

TL;DR

This paper introduces first-order convex feasibility algorithms, including an accelerated Chambolle-Pock method, to improve iterative image reconstruction in CT, especially under limited-angle conditions where traditional optimization is challenging.

Contribution

It develops convex feasibility algorithms tailored for CT image reconstruction, offering efficient alternatives to traditional optimization methods and facilitating better algorithm design.

Findings

Accelerated Chambolle-Pock algorithm applied to convex feasibility in CT.

Convex feasibility approach offers alternatives to unconstrained optimization.

Proposed methods improve reconstruction under limited-angle scans.

Abstract

Iterative image reconstruction (IIR) algorithms in Computed Tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this article, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for efficient algorithms for their solution -- thereby facilitating the IIR algorithm design process. An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization.