MARS-MD: rejection based image domain material decomposition

TL;DR

This paper introduces MARS-MD, a rejection-based algorithm for material decomposition in spectral CT that simplifies under-determined problems by splitting, solving, and rejecting solutions, improving sparsity and reducing signal crossover.

Contribution

It presents a novel heuristic approach for material decomposition that handles under-determined problems through sub-problem splitting and rejection, with two specific algorithms.

Findings

Effective in reducing signal crossover between material images

Allows flexible application of constraints to sub-problems

Demonstrates practical utility in spectral CT imaging

Abstract

This paper outlines image domain material decomposition algorithms that have been routinely used in MARS spectral CT systems. These algorithms (known collectively as MARS-MD) are based on a pragmatic heuristic for solving the under-determined problem where there are more materials than energy bins. This heuristic contains three parts: (1) splitting the problem into a number of possible sub-problems, each containing fewer materials; (2) solving each sub-problem; and (3) applying rejection criteria to eliminate all but one sub-problem's solution. An advantage of this process is that different constraints can be applied to each sub-problem if necessary. In addition, the result of this process is that solutions will be sparse in the material domain, which reduces crossover of signal between material images. Two algorithms based on this process are presented: the Segmentation variant, which uses segmented material classes to define each sub-problem; and the Angular Rejection variant, which defines the rejection criteria using the angle between reconstructed attenuation vectors.