Blind beam-hardening correction from Poisson measurements
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We develop a sparse image reconstruction method for Poisson-distributed polychromatic X-ray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. We employ our mass-attenuation spectrum parameterization of the noiseless measurements and express the mass- attenuation spectrum as a linear combination of B-spline basis functions of order one. A block coordinate-descent algorithm is developed for constrained minimization of a penalized Poisson negative log-likelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density map image; the image sparsity is imposed using a convex total-variation (TV) norm penalty term. This algorithm alternates between a Nesterov’s proximal-gradient (NPG) step for estimating the density map image and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) step for estimating the incident-spectrum parameters. To accelerate convergence of the density- map NPG steps, we apply function restart and a step-size selection scheme that accounts for varying local Lipschitz constants of the Poisson NLL. Real X-ray CT reconstruction examples demonstrate the performance of the proposed scheme.
This proceeding may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This proceeding appeared in Gu, Renliang, and Aleksandar Dogandžić. "Blind beam-hardening correction from Poisson measurements." In AIP Conference Proceedings, vol. 1706, no. 1, p. 110010. AIP Publishing LLC, 2016, and may be found at DOI: 10.1063/1.4940581. Copyright 2016 AIP Publishing LLC. Posted with permission.