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.

翻译：多能计算断层成像(ME-CT)是一种X射线传输成像技术,它利用X射线光子衰减的能量依赖性确定一个受关注对象的元素构成。从数学角度讲,前方的ME-CT测量用非线性整体变异模型模型进行。本文研究了ME-CT变异全球可视性的当地条件,并提供了从测量到重建的错误传播量的明确稳定估计值。从ME-CT图像重建的反面问题中激发了动力,提出了所谓的P功能的迭代反演算法。在两个和三个能源测量数量相同的材料环境中,对ME-CT的数值模拟证实了理论预测。