Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem

Authors:
Xiaowei He;Jimin Liang;Xiaochao Qu;Heyu Huang;Yanbin Hou;Jie Tian
Affiliations:
Life Sciences Research Center, School of Life Sciences and Technology, Xidian University, Xi'an, China and School of Information Sciences and Technology, Northwest University, Xi'an, Shaanxi, Chin ...;Life Sciences Research Center, School of Life Sciences and Technology, Xidian University, Xi'an, China;Life Sciences Research Center, School of Life Sciences and Technology, Xidian University, Xi'an, China;Life Sciences Research Center, School of Life Sciences and Technology, Xidian University, Xi'an, China;Life Sciences Research Center, School of Life Sciences and Technology, Xidian University, Xi'an, China;Life Sciences Research Center, School of Life Sciences and Technology, Xidian University, Xi'an, China and Institute of Automation, Chinese Academy of Sciences, Beijing, China
Venue:
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Year:
2010

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Abstract

In bioluminescence tomography (BLT), reconstruction of internal bioluminescent source distribution from the surface optical signals is an ill-posed inverse problem. In real BLT experiment, apart from the measurement noise, the system errors caused by geometry mismatch, numerical discretization, and optical modeling approximations are also inevitable, which may lead to large errors in the reconstruction results. Most regularization techniques such as Tikhonov method only consider measurement noise, whereas the influences of system errors have not been investigated. In this paper, the truncated total least squares method (TTLS) is introduced into BLT reconstruction, in which both system errors and measurement noise are taken into account. Based on the modified generalized cross validation (MGCV) criterion and residual error minimization, a practical parameter-choice scheme referred to as improved GCV (IGCV) is proposed for TTLS. Numerical simulations with different noise levels and physical experiments demonstrate the effectiveness and potential of TTLS combined with IGCV for solving the BLT inverse problem.