Abstract
Optimization-based algorithms for image reconstruction in multispectral (or photon-counting) computed tomography (MCT) remains a topic of active research. The challenge of optimization-based image reconstruction in MCT stems from the inherently non-linear data model that can lead to a non-convex optimization program for which no mathematically exact solver seems to exist for achieving globally optimal solutions. In this work, based upon a non-linear data model, we design a non-convex optimization program, derive its first-order-optimality conditions, and propose an algorithm to solve the program for image reconstruction in MCT. In addition to consideration of image reconstruction for the standard scan configuration, the emphasis is on investigating the algorithm's potential for enabling non-standard scan configurations with no or minimum hardware modification to existing CT systems, which has potential practical implications for lowered hardware cost, enhanced scanning flexibility, and reduced imaging dose/time in MCT. Numerical studies are carried out for verification of the algorithm and its implementation, and for a preliminary demonstration and characterization of the algorithm in reconstructing images and in enabling non-standard configurations with varying scanning angular range and/or x-ray illumination coverage in MCT.