A potential application for spectral computed tomography (CT) with multi-energy-window photon-counting detectors is quantitative medical imaging with K-edge contrast agents. Image reconstruction for spectral CT with such contrast agents necessitates expression of the X-ray linear attenuation map in at least three expansion functions, for example, bone/water/K-edge-material or photo-electric- process/Compton-process/K-edge-material. The use of three expansion functions can result in slow convergence for iterative image reconstruction (IIR) algorithms applied to spectral CT. We propose a block-diagonal step-preconditioner for use with a primal-dual iterative image reconstruction framework that we have been developing for spectral CT. We demonstrate the advantage of the new step-preconditioner on a sensitive spectral CT simulation where the test object has low concentration of Gadolinium (Gd) contrast agent and the X-ray attenuation map is represented by three materials - PMMA, a soft-tissue equivalent, Aluminum, a bone equivalent, and Gd.
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