We develop a framework for reconstructing images that are sparse in an appropriate transform domain from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and incidentenergy spectrum are unknown. Assuming that the object that we wish to reconstruct consists of a single material, we obtain a parsimonious measurementmodel parameterization 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 Laplaceintegral form. Themore »
Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via Bspline basis function expansion
We develop a sparse image reconstruction method for polychromatic 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 massattenuation spectrum is expanded into basis functions using a Bspline basis of order one. We develop a block coordinatedescent algorithm for constrained minimization of a penalized negative loglikelihood 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 proximalgradient step for estimating the density map image and an activeset step for estimating the incident spectrum parameters. Numerical simulations demonstrate the performance of the proposed scheme.
 Award ID(s):
 1421480
 Publication Date:
 NSFPAR ID:
 10012984
 Journal Name:
 AIP conference proceedings
 Volume:
 34 1650
 ISSN:
 0094243X
 Sponsoring Org:
 National Science Foundation
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