Notes on the primal-dual algorithm for convex optimization applied to X-ray tomographic image reconstruction

TL;DR

This paper explains the primal-dual algorithm by Chambolle and Pock for convex optimization in X-ray tomography, emphasizing intuition, pre-conditioning, and foundational concepts for imaging scientists.

Contribution

It offers a self-contained, intuitive overview of the primal-dual algorithm tailored for imaging applications, with insights on pre-conditioning and convex analysis.

Findings

Provides a clear, accessible explanation of the primal-dual algorithm

Highlights the importance of pre-conditioning in convex optimization

Serves as a foundational resource for imaging scientists

Abstract

The purpose of these notes is to provide background on understanding the primal-dual algorithm of Chambolle and Pock [1] for imaging scientists. The presentation focuses on providing intuition and an algorithmic system that is amenable to pre-conditioning. The document aims to be self-contained, providing background on the essential facts of non-smooth convex analysis.[2]