Alternating Minimization for Computed Tomography with Unknown Geometry Parameters

TL;DR

This paper introduces an alternating minimization algorithm for CT image reconstruction that effectively handles unknown geometry parameters, with demonstrated numerical improvements and a survey of acceleration techniques.

Contribution

The paper presents a novel alternating minimization approach for CT reconstruction with unknown geometry, including convergence acceleration strategies and implementation insights.

Findings

The algorithm effectively reconstructs images with perturbed geometry parameters.

Numerical experiments show improved reconstruction quality.

Surveyed methods enhance convergence speed.

Abstract

Due to the COVID-19 pandemic, there is an increasing demand for portable CT machines worldwide in order to diagnose patients in a variety of settings. This has led to a need for CT image reconstruction algorithms that can produce high quality images in the case when multiple types of geometry parameters have been perturbed. In this paper we present an alternating minimization algorithm to address this issue, where one step minimizes a regularized linear least squares problem, and the other step minimizes a bounded non-linear least squares problem. Additionally, we survey existing methods to accelerate convergence of the algorithm and discuss implementation details. Finally, numerical experiments are conducted to illustrate the effectiveness of the algorithm.