Analysis of finite-element-based methods for reducing the ill-posedness in the reconstruction of fluorescence molecular tomography  

作　　者：Zhun Xu, Jing Bai Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing 100084, China 

出　　处：《Progress in Natural Science:Materials International》2009年第4期501-509,共9页自然科学进展·国际材料（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 30670577,60571013, 60331010);the National Basic Research Program of China (Grant No. 2006CB705700);the Hi-Tech Research and Development Program of China (GrantNo. 2006AA020803)

摘　　要：The major issue in reconstruction of optical imaging might be the ill-posedness of the problem. In this paper, four different algorithms, including singular value decomposition (SVD), the truncated SVD, Tikhonov regularization and adaptive regularization, are analyzed and applied for solving the matrix equation generated from diffuse equation based on finite-element method in fluorescence molecular tomography. Results illustrate the need for either imposition of regularization term or elimination of too small singular values in reducing the illposedness. The results also suggest that the adaptive-regularization method offers superior performance in the reconstruction among the four methods in most cases even if the initially selected regularization parameter is not optimal, thus providing the convenience for the reconstruction.The major issue in reconstruction of optical imaging might be the ill-posedness of the problem. In this paper, four different algorithms, including singular value decomposition （SVD）, the truncated SVD, Tikhonov regularization and adaptive regularization, are analyzed and applied for solving the matrix equation generated from diffuse equation based on finite-element method in fluorescence molecular tomography. Results illustrate the need for either imposition of regularization term or elimination of too small singular values in reduc- ing the ill-posedness. The results also suggest that the adaptive-regularization method offers superior performance in the reconstruction among the four methods in most cases even if the initially selected regularization parameter is not optimal, thus providing the conve- nience for the reconstruction.

关 键 词：Fluorescence molecular tomography RECONSTRUCTION ILL-POSEDNESS The truncated SVD Adaptive regularization 

分 类 号：O241.82[理学—计算数学]