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An Investigation of Direct Image Reconstruction in DECT with Physical Data

Non-convex optimization problems, such as those based on a non-linear data model in multispectral CT, can not be solved by directly applying the first-order primal-dual Chambolle-Pock (CP) algorithm. In this work, we propose a non-convex primal-dual algorithm, inspired by our previous work on the ASD-NC-POCS algorithm for the non-convex constrained TV-minimization problem in multispectral CT. The proposed non-convex CP (ncCP) algorithm can accommodate different optimization program designs including non-smooth objectives and/or constraints, and also involves relatively fewer parameters. It is different than the MOCCA algorithm, which is also an extension of the primal-dual CP algorithm, in the sense that ncCP uses a global linear approximation to the data model and estimates the non-linear term locally, whereas MOCCA uses a local quadratic convex approximation to the data fidelity term. An algorithm instance of the proposed ncCP algorithm for a non-convex optimization problem in dual-energy CT has been derived and applied to physical head phantom data collected on a clinical scanner. Comparable basis and monochromatic images can be observed from the ncCP algorithm and the standard, data-domain decomposition method, in this preliminary study with two-full-rotation dual-energy data of overlapping rays.