An algorithm for constrained one-step inversion of spectral CT data

TL;DR

This paper introduces a primal-dual algorithm for direct spectral CT image reconstruction that enforces constraints during inversion, demonstrating convergence and effectiveness on simulated data with noise and phantoms.

Contribution

A novel primal-dual optimization algorithm enabling constrained one-step spectral CT data inversion with proven convergence.

Findings

Algorithm successfully reconstructs basis maps from simulated spectral CT data.

Constraints improve image quality and fidelity in reconstructions.

Demonstrated robustness with noisy data and complex phantoms.

Abstract

We develop a primal-dual algorithm that allows for one-step inversion of spectral CT transmission photon counts data to a basis map decomposition. The algorithm allows for image constraints to be enforced on the basis maps during the inversion. The derivation of the algorithm makes use of a local upper bounding quadratic approximation to generate descent steps for non-convex spectral CT data discrepancy terms, combined with a new convex-concave optimization algorithm. Convergence of the algorithm is demonstrated on simulated spectral CT data. Simulations with noise and anthropomorphic phantoms show examples of how to employ the constrained one-step algorithm for spectral CT data.