Multi-Channel Potts-Based Reconstruction for Multi-Spectral Computed Tomography

TL;DR

This paper introduces a multi-channel Potts prior for multi-spectral CT image reconstruction, leveraging structural correlations to improve edge alignment across channels compared to traditional TV methods.

Contribution

It develops and compares variational and superiorization-based Potts prior methods, demonstrating improved multi-channel image reconstruction over existing TV-based approaches.

Findings

Potts prior methods outperform TV methods in multi-spectral CT reconstruction.

ADMM and Potts-superiorized conjugate gradient are effective algorithms.

Numerical experiments show improved reconstruction quality for complex solid bodies.

Abstract

We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral X-ray computed tomography (CT). Our aim is to exploit the strong structural correlation that is known to exist between the channels of multi-spectral CT images. To that end, we adopt the multi-channel Potts prior to jointly reconstruct all channels. This prior produces piecewise constant solutions with strongly correlated channels. In particular, edges are enforced to have the same spatial position across channels which is a benefit over TV-based methods. We consider the Potts prior in two frameworks: (a) in the context of a variational Potts model, and (b) in a Potts-superiorization approach that perturbs the iterates of a basic iterative least squares solver. We identify an alternating direction method of multipliers (ADMM) approach as well as a Potts-superiorized conjugate gradient method as particularly suitable. In numerical experiments, we compare the Potts prior based approaches to existing TV-type approaches on realistically simulated multi-spectral CT data and obtain improved reconstruction for compound solid bodies.