skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion

Abstract

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-attenuation spectrum 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.

Authors:
;  [1]
  1. Iowa State University, Center for Nondestructive Evaluation, 1915 Scholl Road, Ames, IA 50011 (United States)
Publication Date:
OSTI Identifier:
22391228
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1650; Journal Issue: 1; Conference: 41. Annual Review of Progress in Quantitative Nondestructive Evaluation, Boise, ID (United States), 20-25 Jul 2014; Other Information: (c) 2015 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; ALGORITHMS; ATTENUATION; COMPUTERIZED SIMULATION; COMPUTERIZED TOMOGRAPHY; ENERGY SPECTRA; IMAGE PROCESSING; INTEGRALS; LIMITING VALUES; MATHEMATICAL MODELS; PERFORMANCE; SPLINE FUNCTIONS

Citation Formats

Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu, and Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu. Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion. United States: N. p., 2015. Web. doi:10.1063/1.4914792.
Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu, & Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu. Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion. United States. doi:10.1063/1.4914792.
Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu, and Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu. Tue . "Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion". United States. doi:10.1063/1.4914792.
@article{osti_22391228,
title = {Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion},
author = {Gu, Renliang, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu and Dogandžić, Aleksandar, E-mail: Venliang@iastate.edu, E-mail: ald@iastate.edu},
abstractNote = {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-attenuation spectrum 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.},
doi = {10.1063/1.4914792},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1650,
place = {United States},
year = {Tue Mar 31 00:00:00 EDT 2015},
month = {Tue Mar 31 00:00:00 EDT 2015}
}