Journal article
A New Coupled Complex Boundary Method for Bioluminescence Tomography
Communications in computational physics, Vol.19(1), pp.226-250
01/01/2016
DOI: 10.4208/cicp.230115.150615a
Abstract
In this paper, we introduce and study a new method for solving inverse source problems, through a working model that arises in bioluminescence tomography (BLT). In the 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 possesses strong ill-posedness 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 for trade off between the accuracy and stability of approximate solutions. The new method is based on a combination of the boundary condition and the boundary measurement in a parameter-dependent single complex Robin boundary condition, followed by the Tikhonov regularization. By properly adjusting the parameter in the Robin boundary condition, we achieve two important properties for our new method: first, 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; second, the convergence order of the regularized solutions reaches one with respect to the noise level. Then, the finite element method is used to compute numerical solutions and a new finite element error estimate is derived for discrete solutions. These results improve related results found in the existing literature. Several numerical examples are provided to illustrate the theoretical results.
Details
- Title: Subtitle
- A New Coupled Complex Boundary Method for Bioluminescence Tomography
- Creators
- Rongfang Gong - Nanjing UniversityXiaoliang Cheng - Zhejiang UniversityWeimin Han - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Communications in computational physics, Vol.19(1), pp.226-250
- Publisher
- GLOBAL SCIENCE PRESS
- DOI
- 10.4208/cicp.230115.150615a
- ISSN
- 1815-2406
- eISSN
- 1991-7120
- Number of pages
- 25
- Grant note
- NS2014078 / Fundamental Research Funds for the Central Universities 91130004 / Key Project of the Major Research Plan of NSFC BK20130780 / Natural Science Foundation of Jiangsu Province 11401304 / Natural Science Foundation of China 207052; 228187 / Simons Foundation DMS-1521684 / NSF
- Language
- English
- Date published
- 01/01/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984240877402771
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