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Computational and Mathematical Methods in Medicine
Volume 2015 (2015), Article ID 286161, 23 pages
http://dx.doi.org/10.1155/2015/286161
Research Article

Image Reconstruction for Diffuse Optical Tomography Based on Radiative Transfer Equation

1Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150006, China
2School of Mathematics and Statistics, Northeast Petroleum University, Daqing, Heilongjiang 163318, China
3Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
4Imaging Diagnosis and Interventional Center, State Key Laboratory of Oncology in South China, Sun Yat-sen University Cancer Center, Guangzhou, Guangdong 510060, China

Received 5 October 2014; Revised 8 December 2014; Accepted 17 December 2014

Academic Editor: Reinoud Maex

Copyright © 2015 Bo Bi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Diffuse optical tomography is a novel molecular imaging technology for small animal studies. Most known reconstruction methods use the diffusion equation (DA) as forward model, although the validation of DA breaks down in certain situations. In this work, we use the radiative transfer equation as forward model which provides an accurate description of the light propagation within biological media and investigate the potential of sparsity constraints in solving the diffuse optical tomography inverse problem. The feasibility of the sparsity reconstruction approach is evaluated by boundary angular-averaged measurement data and internal angular-averaged measurement data. Simulation results demonstrate that in most of the test cases the reconstructions with sparsity regularization are both qualitatively and quantitatively more reliable than those with standard regularization. Results also show the competitive performance of the split Bregman algorithm for the DOT image reconstruction with sparsity regularization compared with other existing algorithms.