Polychromatic Sparse Image Reconstruction and Mass Attenuation Spectrum Estimation via B-spline Basis Function Expansion
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We develop a sparse image reconstruction method for polychromatic 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 measurement model parameterization, we first rewrite the measurement equation using our mass-attenuation parameterization, which has the Laplace integral form. The unknown mass-attenuationspectrum is expanded into basis functions using a B-spline basis of order one. We develop a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and sparsity of the density map image in the wavelet domain. This algorithm alternates between a Nesterov’s proximal-gradient step for estimating the density map image and an active-set step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme.
The following article appeared in AIP Conference Proceedings 1650 (2015): 1707, doi:10.1063/1.4914792 and may be found at http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4914792.