Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm

TL;DR

This paper demonstrates how the Chambolle-Pock primal-dual algorithm can be used as a flexible tool for rapid prototyping of convex optimization models in computed tomography image reconstruction, including applications to breast CT.

Contribution

It introduces a systematic approach to derive specific algorithm instances for various CT reconstruction problems using the Chambolle-Pock method.

Findings

The algorithm enables quick development of CT reconstruction methods.

Explicit derivations for multiple CT optimization problems are provided.

Application to low-intensity breast CT shows practical relevance.

Abstract

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented.