An inversion algorithm for P-functions with applications to multi-energy CT. (7th February 2022)

• Record Type: Journal Article
• Authors: Bal, Guillaume; Gong, Ruoming; Terzioglu, Fatma
• Is Part Of: Inverse problems. Volume 38:Number 3(2022)
• Publication Date: 2022-02-07
• Subjects: P-function -- inversion -- global -- uniqueness -- stability -- multi-energy CT -- spectral CT; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac4d0a
• Languages: English
• ISSNs: 0266-5611

Abstract

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.