Journal article
A fast solver for an inverse problem arising in bioluminescence tomography
Journal of computational and applied mathematics, Vol.267, pp.228-243
09/2014
DOI: 10.1016/j.cam.2014.02.014
Abstract
Bioluminescence tomography (BLT) is a new method in biomedical imaging, with a promising potential in monitoring non-invasively physiological and pathological processes in vivo at the cellular and molecular levels. The goal of BLT is to quantitatively reconstruct a three dimensional bioluminescent source distribution within a small animal from two dimensional optical signals on the surface of the animal body. Mathematically, BLT is an under-determined inverse source problem and is severely ill-posed, making its numerical treatments very challenging. In this paper, we provide a new Tikhonov regularization framework for the BLT problem. Compared with the existing reconstruction methods about BLT, our new method uses an energy functional defined over the whole problem domain for measuring the data fitting, associated with two related but different boundary value problems. Based on the new formulation, a fast solver is introduced by transforming the proposed optimization model into a system of partial differential equations. Moreover, a finite element method is used to obtain a regularized discrete solution. Finally, numerical results show that the fast solver for BLT is feasible and effective.
Details
- Title: Subtitle
- A fast solver for an inverse problem arising in bioluminescence tomography
- Creators
- Rongfang Gong - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, ChinaXiaoliang Cheng - Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaWeimin Han - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
- Resource Type
- Journal article
- Publication Details
- Journal of computational and applied mathematics, Vol.267, pp.228-243
- DOI
- 10.1016/j.cam.2014.02.014
- ISSN
- 0377-0427
- eISSN
- 1879-1778
- Publisher
- Elsevier B.V
- Grant note
- name: natural science foundation of Jiangsu Province, award: BK20130780; DOI: 10.13039/501100012226, name: Fundamental Research Funds for the Central Universities, award: NS2012063; name: Key Project of the Major Research Plan of NSFC, award: 91130004; DOI: 10.13039/100000893, name: Simons Foundation
- Language
- English
- Date published
- 09/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983985993702771
Metrics
41 Record Views