Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method

被引:50
作者
Zhu, WW
Wang, Y
Yao, YQ
Chang, JH
Graber, HL
Barbour, RL
机构
[1] POLYTECH INST NEW YORK,DEPT ELECT ENGN,BROOKLYN,NY 11201
[2] SUNY HLTH SCI CTR,DEPT PATHOL,BROOKLYN,NY 11203
[3] SUNY HLTH SCI CTR,DEPT BIOPHYS,BROOKLYN,NY 11203
来源
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION | 1997年 / 14卷 / 04期
关键词
image reconstruction; total least squares; medical optical tomography; conjugate gradient method;
D O I
10.1364/JOSAA.14.000799
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We present an iterative total least-squares algorithm for computing images of the interior structure of highly scattering media by using the conjugate gradient method. For imaging the dense scattering media in optical tomography, a perturbation approach has been described previously [T. Wang et al., Proc. SPIE 1641, 58 (1992); R. L. Barbour et al., in Medical Optical Tomography: Functional Imaging and Monitoring (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87-120], which solves a perturbation equation of the form W Delta x = Delta I. In order to solve this equation, least-squares or regularized least-squares solvers have been used in the past to determine best fits to the measurement data Delta I while assuming that the operator matrix W is accurate. In practice, errors also occur in the operator matrix. Here we propose an iterative total least-squares (ITLS) method that minimizes the errors in both weights and detector readings. Theoretically, the total least-squares (TLS) solution is given by the singular vector of the matrix [W\Delta I] associated with the smallest singular value. The proposed ITLS method obtains this solution by using a conjugate gradient method that is particularly suitable for very large matrices. Simulation results have shown that the TLS method can yield a significantly more accurate result than the least-squares method. (C) 1997 Optical Society of America.
引用
收藏
页码:799 / 807
页数:9
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