Campus Units

Electrical and Computer Engineering

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

6-2016

Journal or Book Title

IEEE Transactions on Computational Imaging

Volume

2

Issue

2

First Page

150

Last Page

165

DOI

10.1109/TCI.2016.2523431

Abstract

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 incident-energy spectrum are unknown. Assuming that the object that we wish to reconstruct consists of a single material, we obtain a parsimonious measurement-model 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 mass-attenuation spectrum function; the resulting measurement equation has the Laplaceintegral form. The mass-attenuation 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 log-likelihood (NLL) function with respect to the density-map and mass-attenuation spectrum parameters. We derive a block-coordinate descent algorithm for constrained minimization of a penalized NLL objective function, where penalty terms ensure nonnegativity of the mass-attenuation spline coefficients and nonnegativity and gradient-map sparsity of the density-map image, imposed using a convex total-variation (TV) norm; the resulting objective function is biconvex. This algorithm alternates between a Nesterov’s proximal-gradient (NPG) step and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGSB) iteration for updating the image and mass-attenuation spectrum parameters, respectively. We prove the Kurdyka-Łojasiewicz property of the objective function, which is important for establishing local convergence of block-coordinate descent schemes in biconvex optimization problems. Our framework applies to other NLLs and signal-sparsity penalties, such as lognormal NLL and `1 norm of 2D discrete wavelet transform (DWT) image coefficien- s. Numerical experiments with simulated and real X-ray CT data demonstrate the performance of the proposed scheme.

Comments

This is a manuscript of an article from IEEE Transactions on Computational Imaging 2 (2016): 150, doi:10.1109/TCI.2016.2523431. Posted with permission.

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Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Copyright Owner

IEEE

Language

en

File Format

application/pdf

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