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Title: Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization

Abstract

We propose a method for reconstructing sparse images from polychromatic x-ray computed tomography (ct) measurements via mass attenuation coefficient discretization. The material of the inspected object and the incident spectrum are assumed to be unknown. We rewrite the Lambert-Beer’s law in terms of integral expressions of mass attenuation and discretize the resulting integrals. We then present a penalized constrained least-squares optimization approach for reconstructing the underlying object from log-domain measurements, where an active set approach is employed to estimate incident energy density parameters and the nonnegativity and sparsity of the image density map are imposed using negative-energy and smooth ℓ{sub 1}-norm penalty terms. We propose a two-step scheme for refining the mass attenuation discretization grid by using higher sampling rate over the range with higher photon energy, and eliminating the discretization points that have little effect on accuracy of the forward projection model. This refinement allows us to successfully handle the characteristic lines (Dirac impulses) in the incident energy density spectrum. We compare the proposed method with the standard filtered backprojection, which ignores the polychromatic nature of the measurements and sparsity of the image density map. Numerical simulations using both realistic simulated and real x-ray ct data are presented.

Authors:
;  [1]
  1. Iowa State University, Center for Nondestructive Evaluation, 1915 Scholl Road, Ames, IA 50011 (United States)
Publication Date:
OSTI Identifier:
22263776
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1581; Journal Issue: 1; Conference: 40. annual review of progress in quantitative nondestructive evaluation, Baltimore, MD (United States), 21-26 Jul 2013, 10. international conference on Barkhausen noise and micromagnetic testing, Baltimore, MD (United States), 21-26 Jul 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ATTENUATION; CHARGES; COMPUTERIZED SIMULATION; COMPUTERIZED TOMOGRAPHY; ENERGY DENSITY; GRIDS; INTEGRALS; LEAST SQUARE FIT; OPTIMIZATION; PULSES; SIGNALS; SPECTRA; X RADIATION

Citation Formats

Gu, Renliang, and Dogandžić, Aleksandar. Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization. United States: N. p., 2014. Web. doi:10.1063/1.4865048.
Gu, Renliang, & Dogandžić, Aleksandar. Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization. United States. doi:10.1063/1.4865048.
Gu, Renliang, and Dogandžić, Aleksandar. 2014. "Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization". United States. doi:10.1063/1.4865048.
@article{osti_22263776,
title = {Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization},
author = {Gu, Renliang and Dogandžić, Aleksandar},
abstractNote = {We propose a method for reconstructing sparse images from polychromatic x-ray computed tomography (ct) measurements via mass attenuation coefficient discretization. The material of the inspected object and the incident spectrum are assumed to be unknown. We rewrite the Lambert-Beer’s law in terms of integral expressions of mass attenuation and discretize the resulting integrals. We then present a penalized constrained least-squares optimization approach for reconstructing the underlying object from log-domain measurements, where an active set approach is employed to estimate incident energy density parameters and the nonnegativity and sparsity of the image density map are imposed using negative-energy and smooth ℓ{sub 1}-norm penalty terms. We propose a two-step scheme for refining the mass attenuation discretization grid by using higher sampling rate over the range with higher photon energy, and eliminating the discretization points that have little effect on accuracy of the forward projection model. This refinement allows us to successfully handle the characteristic lines (Dirac impulses) in the incident energy density spectrum. We compare the proposed method with the standard filtered backprojection, which ignores the polychromatic nature of the measurements and sparsity of the image density map. Numerical simulations using both realistic simulated and real x-ray ct data are presented.},
doi = {10.1063/1.4865048},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1581,
place = {United States},
year = 2014,
month = 2
}
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