An Efficient One-Step Method for Spectral CT Based on an Approximate Linear Model

Spectral computed tomography (spectral CT) is a medical and biomedical imaging technique which uses the spectral information of the attenuated X-ray beam. Energy-resolved photon-counting detector is a promising technique for improved spectral CT imaging and allows to obtain material selective images. Two different kind of approaches can be used to solve the problem of spectral reconstruction consisting of material decomposition and tomographic reconstruction: the “two steps” methods which are most often projection-based methods, and the “one step” methods. While the projection-based methods are interesting for the fast computational time, the one-step methods link directly the material image domain and the multienergy sinograms domain, which is an advantage to introduce spatial prior information in the material image domain. In this work we propose a proximal operator associated to a data fidelity term (based on an empirical linear forward model) for multimaterial decomposition. This proximal operator, which has a closed-form solution, makes it possible to propose fast regularized reconstruction methods for spectral CT, in particular for data of photon-counting detectors with many energy bins. We propose a one-step method based on the alternating direction method of multipliers (ADMM) and this proximal operator. We present promising results on dual material image reconstructions obtained from simulated and experimental data. We show qualitative and quantitative comparisons with two previously published multimaterial decomposition methods.