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Title: Inverse transport calculations in optical imaging with subspace optimization algorithms

Abstract

Inverse boundary value problems for the radiative transport equation play an important role in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid progress in the mathematical theory and numerical computation of these inverse problems in recent years, developing robust and efficient reconstruction algorithms remains a challenging task and an active research topic. We propose here a robust reconstruction method that is based on subspace minimization techniques. The method splits the unknown transport solution (or a functional of it) into low-frequency and high-frequency components, and uses singular value decomposition to analytically recover part of low-frequency information. Minimization is then applied to recover part of the high-frequency components of the unknowns. We present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm.

Authors:
;
Publication Date:
OSTI Identifier:
22382104
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 273; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; BOUNDARY-VALUE PROBLEMS; CALCULATION METHODS; COMPUTERIZED SIMULATION; FLUORESCENCE; MATHEMATICAL SOLUTIONS; MINIMIZATION; OPTICS; PERFORMANCE; TOMOGRAPHY; TRANSPORT THEORY

Citation Formats

Ding, Tian, E-mail: tding@math.utexas.edu, and Ren, Kui, E-mail: ren@math.utexas.edu. Inverse transport calculations in optical imaging with subspace optimization algorithms. United States: N. p., 2014. Web. doi:10.1016/J.JCP.2014.05.014.
Ding, Tian, E-mail: tding@math.utexas.edu, & Ren, Kui, E-mail: ren@math.utexas.edu. Inverse transport calculations in optical imaging with subspace optimization algorithms. United States. doi:10.1016/J.JCP.2014.05.014.
Ding, Tian, E-mail: tding@math.utexas.edu, and Ren, Kui, E-mail: ren@math.utexas.edu. Mon . "Inverse transport calculations in optical imaging with subspace optimization algorithms". United States. doi:10.1016/J.JCP.2014.05.014.
@article{osti_22382104,
title = {Inverse transport calculations in optical imaging with subspace optimization algorithms},
author = {Ding, Tian, E-mail: tding@math.utexas.edu and Ren, Kui, E-mail: ren@math.utexas.edu},
abstractNote = {Inverse boundary value problems for the radiative transport equation play an important role in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid progress in the mathematical theory and numerical computation of these inverse problems in recent years, developing robust and efficient reconstruction algorithms remains a challenging task and an active research topic. We propose here a robust reconstruction method that is based on subspace minimization techniques. The method splits the unknown transport solution (or a functional of it) into low-frequency and high-frequency components, and uses singular value decomposition to analytically recover part of low-frequency information. Minimization is then applied to recover part of the high-frequency components of the unknowns. We present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm.},
doi = {10.1016/J.JCP.2014.05.014},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 273,
place = {United States},
year = {2014},
month = {9}
}