An inversion algorithm for P-functions with applications to Multi-energy CT

TL;DR

This paper develops an iterative inversion algorithm for P-functions in multi-energy CT, providing conditions for invertibility, stability estimates, and numerical validation in multi-material scenarios.

Contribution

It introduces a new iterative inversion method for P-functions in ME-CT and analyzes conditions for invertibility and stability.

Findings

Theoretical invertibility conditions are established.

Stability estimates for the inversion process are derived.

Numerical simulations confirm the effectiveness of the proposed algorithm.

Abstract

Multi-energy computed tomography (ME-CT) is an x-ray transmission imaging technique that uses the energy dependence of x-ray photon attenuation to determine the elemental composition of an object of interest. Mathematically, forward ME-CT measurements are modeled by a nonlinear integral transform. In this paper, local conditions for global invertibility of the ME-CT transform are studied, and explicit stability estimates quantifying the error propagation from measurements to reconstructions are provided. Motivated from the inverse problem of image reconstruction in ME-CT, an iterative inversion algorithm for the so-called P-functions is proposed. Numerical simulations for ME-CT, in two and three materials settings with an equal number of energy measurements, confirm the theoretical predictions.