Zhu W, Wang Y, Yao Y, Chang J, Graber H L, Barbour R L
Department of Electrical Engineering, Polytechnic University, Brooklyn, New York 11201, USA.
J Opt Soc Am A Opt Image Sci Vis. 1997 Apr;14(4):799-807. doi: 10.1364/josaa.14.000799.
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.
我们提出了一种迭代总体最小二乘法算法，用于通过共轭梯度法计算高散射介质内部结构的图像。对于光学层析成像中密集散射介质的成像，之前已经描述了一种微扰方法[Y. Wang等人，《光学工程学会会刊》1641, 58 (1992); R. L. Barbour等人，《医学光学层析成像：功能成像与监测》（光电仪器工程师协会，华盛顿州贝灵汉，1993年），第87 - 120页]，该方法求解形如Wδx = δI的微扰方程。为了求解此方程，过去使用最小二乘法或正则化最小二乘法求解器来确定与测量数据δI的最佳拟合，同时假设算子矩阵W是准确的。实际上，算子矩阵中也会出现误差。在此，我们提出一种迭代总体最小二乘（ITLS）方法，该方法可使权重和探测器读数中的误差最小化。从理论上讲，总体最小二乘（TLS）解由与最小奇异值相关联的矩阵[W / δI]的奇异向量给出。所提出的ITLS方法通过使用特别适用于非常大矩阵的共轭梯度法来获得此解。仿真结果表明，TLS方法比最小二乘法能产生显著更准确的结果。
