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

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