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

W. Zhu et al. (1997)


We present an iterative total least–squares algorithm for computing images of the interior of highly scattering media by using the conjugate gradient method. For imaging of 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 WΔx = ΔI. 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 [WI] 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.