Alternating Minimization for Computed Tomography with Unknown Geometry Parameters

TL;DR

This paper tackles CT image reconstruction when geometry parameters are unknown, as in portable CT devices. It proposes an alternating minimization framework that alternates between a regularized linear LS step for the image and a bounded nonlinear LS step for geometry, using $A(p)$ to encode geometry. The authors survey acceleration techniques (e.g., Anderson acceleration, fixed-point methods) and implement parallelization, leveraging IRtools solvers and implicit filtering. Results on phantom and spine images demonstrate substantial speedups and improved convergence with acceleration, with solver choice depending on the perturbation size.

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.

Figures (14)

• Figure 1: Object-Source-Detector
• Figure 2: Beer's Law for a Single Material Object
• Figure 3: Beer's Law for an Object of Multiple Materials
• Figure 4: Fan-beam X-rays
• Figure 5: Graphs Comparing Acceleration Techniques