Non-convex primal-dual algorithm for image reconstruction in spectral CT

TL;DR

This paper introduces a non-convex primal-dual algorithm for spectral CT image reconstruction that directly inverts the non-linear data model, enabling accurate monochromatic imaging even with non-standard scan configurations.

Contribution

The paper develops a novel non-convex primal-dual algorithm for spectral CT reconstruction, capable of directly solving the non-linear data model and handling non-standard scanning geometries.

Findings

Successfully reconstructs monochromatic images from simulated and real data.

Corrects beam-hardening effects accurately in spectral CT images.

Enables non-standard scan configurations with comparable image quality.

Abstract

The work seeks to develop an algorithm for image reconstruction by directly inverting the non-linear data model in spectral CT. Using the non-linear data model, we formulate the image-reconstruction problem as a non-convex optimization program, and develop a non-convex primal-dual (NCPD) algorithm to solve the program. We devise multiple convergence conditions and perform verification studies numerically to demonstrate that the NCPD algorithm can solve the non-convex optimization program and under appropriate data condition, can invert the non-linear data model. Using the NCPD algorithm, we then reconstruct monochromatic images from simulated and real data of numerical and physical phantoms acquired with a standard, full-scan dual-energy configuration. The result of the reconstruction studies shows that the NCPD algorithm can correct accurately for the non-linear beam-hardening effect. Furthermore, we apply the NCPD algorithm to simulated and real data of the numerical and physical phantoms collected with non-standard, short-scan dual-energy configurations, and obtain monochromatic images comparable to those of the standard, full-scan study, thus revealing the potential of the NCPD algorithm for enabling non-standard scanning configurations in spectral CT, where the existing indirect methods are limited.