Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method.
Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method.
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DOI：
10.1364/josaa.14.000799
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发表时间：
1997-04
期刊：
影响因子：
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通讯作者：
Wenwu Zhu;Yao Wang;Yuqi Yao;Jenghwa Chang;H. Graber;R. Barbour
中科院分区：
文献类型：
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作者：
Wenwu Zhu;Yao Wang;Yuqi Yao;Jenghwa Chang;H. Graber;R. Barbour
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 [Y. 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.
