Abstract

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 $\mathbf{W}\mathrm{\Delta }\mathbf{x}=\mathrm{\Delta }\mathbf{I}$. 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 ΔI 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|ΔI] 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.

© 1997 Optical Society of America

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