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The work seeks to develop an algorithm for image reconstruction by directlyinverting the non-linear data model in spectral CT. Using the non-linear datamodel, we formulate the image-reconstruction problem as a non-convexoptimization program, and develop a non-convex primal-dual (NCPD) algorithm tosolve the program. We devise multiple convergence conditions and performverification studies numerically to demonstrate that the NCPD algorithm cansolve the non-convex optimization program and under appropriate data condition,can invert the non-linear data model. Using the NCPD algorithm, we thenreconstruct monochromatic images from simulated and real data of numerical andphysical phantoms acquired with a standard, full-scan dual-energyconfiguration. The result of the reconstruction studies shows that the NCPDalgorithm can correct accurately for the non-linear beam-hardening effect.Furthermore, we apply the NCPD algorithm to simulated and real data of thenumerical and physical phantoms collected with non-standard, short-scandual-energy configurations, and obtain monochromatic images comparable to thoseof the standard, full-scan study, thus revealing the potential of the NCPDalgorithm for enabling non-standard scanning configurations in spectral CT,where the existing indirect methods are limited.

Non-convex primal-dual algorithm for image reconstruction in spectral CT