We develop 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. We employ our massattenuation spectrum parameterization of the noiseless measurements for singlematerial objects and express the massattenuation spectrum as a linear combination of Bspline basis functions of order one. A block coordinatedescent algorithm is developed for constrained minimization of a penalized Poisson negative loglikelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the densitymap image; themore »
Blind Xray CT Image Reconstruction from Polychromatic Poisson Measurements
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. The massattenuation spectrum is then expanded into basis functions using B splines of order one. We consider a Poisson noise model and establish conditions for biconvexity of the corresponding negative loglikelihood (NLL) function with respect to the densitymap and massattenuation spectrum parameters. We derive a blockcoordinate descent algorithm for constrained minimization of a penalized NLL objective function, where penalty terms ensure nonnegativity of the massattenuation spline coefficients and nonnegativity and gradientmap sparsity of the densitymap image, imposed using a convex totalvariation (TV) norm; the resulting objective function is biconvex. This algorithm alternates between a Nesterov’s proximalgradient (NPG) step and a limitedmemory more »
 Award ID(s):
 1421480
 Publication Date:
 NSFPAR ID:
 10013990
 Journal Name:
 IEEE Transactions on Computational Imaging
 Page Range or eLocationID:
 1 to 1
 ISSN:
 23340118
 Sponsoring Org:
 National Science Foundation
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