Joint Reconstruction of Multi-channel, Spectral CT Data via Constrained Total Nuclear Variation Minimization

TL;DR

This paper introduces the use of total nuclear variation (TNV) as a regularizer for multi-channel spectral CT image reconstruction, improving feature preservation by encouraging shared edges across channels.

Contribution

It extends total variation to vector-valued images with TNV, incorporating it into a reconstruction framework and demonstrating its advantages over independent TV methods.

Findings

TNV improves feature preservation at high regularization levels.

Simulation results show better inter-channel coupling with TNV.

TNV encourages shared edges across spectral channels.

Abstract

We explore the use of the recently proposed "total nuclear variation" (TNV) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued images and has the advantage of encouraging common edge locations and a shared gradient direction among image channels. We show how it can be incorporated into a general, data-constrained reconstruction framework and derive update equations based on the first-order, primal-dual algorithm of Chambolle and Pock. Early simulation studies based on the numerical XCAT phantom indicate that the inter-channel coupling introduced by the TNV leads to better preservation of image features at high levels of regularization, compared to independent, channel-by-channel TV reconstructions.