ANALYSIS OF A NUMERICAL METHOD FOR RADIATIVE TRANSFER EQUATION BASED BIOLUMINESCENCE TOMOGRAPHY

Rongfang Gong; Joseph Eichholz; Xiaoliang Cheng; Weimin Han

doi:10.4208/jcm.1607-m2016-0515

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ANALYSIS OF A NUMERICAL METHOD FOR RADIATIVE TRANSFER EQUATION BASED BIOLUMINESCENCE TOMOGRAPHY

Journal article

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ANALYSIS OF A NUMERICAL METHOD FOR RADIATIVE TRANSFER EQUATION BASED BIOLUMINESCENCE TOMOGRAPHY

Rongfang Gong, Joseph Eichholz, Xiaoliang Cheng and Weimin Han

Journal of computational mathematics, Vol.34(6), pp.648-670

01/01/2016

DOI: 10.4208/jcm.1607-m2016-0515

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Abstract

In the bioluminescence tomography (BLT) problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal's body surface. The BLT problem is ill-posed and often the Tikhonov regularization is used to obtain stable approximate solutions. In conventional Tikhonov regularization, it is crucial to choose a proper regularization parameter to balance the accuracy and stability of approximate solutions. In this paper, a parameter-dependent coupled complex boundary method (CCBM) based Tikhonov regularization is applied to the BLT problem governed by the radiative transfer equation (RTE). By properly adjusting the parameter in the Robin boundary condition, we achieve one important property: the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy. The discrete-ordinate finite-element method is used to compute numerical solutions. Numerical results are provided to illustrate the performance of the proposed method.

Mathematics

Mathematics, Applied

Physical Sciences

Science & Technology

Details

Title: Subtitle: ANALYSIS OF A NUMERICAL METHOD FOR RADIATIVE TRANSFER EQUATION BASED BIOLUMINESCENCE TOMOGRAPHY
Creators: Rongfang Gong - Nanjing University
Joseph Eichholz - Rose Hulman Inst Technol, Dept Math, Terre Haute, IN 47803 USA
Xiaoliang Cheng - Zhejiang University
Weimin Han - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
Resource Type: Journal article
Publication Details: Journal of computational mathematics, Vol.34(6), pp.648-670
Publisher: GLOBAL SCIENCE PRESS
DOI: 10.4208/jcm.1607-m2016-0515
ISSN: 0254-9409
eISSN: 1991-7139
Number of pages: 23
Grant note: NS2014078 / Fundamental Research Funds for the Central Universities BK20130780 / Natural Science Foundation of Jiangsu Province 11401304 / Natural Science Foundation of China 11571311 / NSFC DMS-1521684 / NSF
Language: English
Date published: 01/01/2016
Academic Unit: Mathematics
Record Identifier: 9984240871602771

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