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I will describe a sparse image reconstruction method for Poissondistributed polychromatic Xray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. To obtain a parsimonious mean measurementmodel parameterization, we first rewrite the measurement equation by changing the integral variable from photon energy to mass attenuation, which allows us to combine the variations brought by the unknown incident spectrum and mass attenuation into a single unknown massattenuation spectrum function; the resulting measurement equation has the Laplace integral form. The massattenuation spectrum is then expanded into basis functions using a Bspline basis of order one. We develop a block coordinatedescent algorithm for minimization of a penalized Poisson negative loglikelihood (NLL) cost function, where penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density map image. This algorithm alternates between a Nesterov’s proximalgradient (NPG) step for estimating the density map image and a limitedmemory Broyden–Fletcher–Goldfarb–Shanno with box constraints (L BFGSB) step for estimating the incidentspectrum parameters. To accelerate convergence of the densitymap NPG steps, we apply a stepsize selection scheme that accounts for varying local Lipschitz constants of the objective function. I will discuss the biconvexity of the penalized NLL function and outline preliminary results on convergence of PGBFGS schemes. Finally, I will present real Xray CT reconstruction examples that demonstrate the performance of the proposed scheme.
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