title: Iterative total least-squares image reconstruction algorithm for optical tomography by the conjugate gradient method.
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 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.
authors.affiliation: Department of Electrical Engineering, Polytechnic University, Brooklyn, New York 11201, USA.
authors.forename: W
authors.initials: W
authors.lastname: Zhu
authors.forename: Y
authors.initials: Y
authors.lastname: Wang
authors.forename: Y
authors.initials: Y
authors.lastname: Yao
authors.forename: J
authors.initials: J
authors.lastname: Chang
authors.forename: H L
authors.initials: HL
authors.lastname: Graber
authors.forename: R L
authors.initials: RL
authors.lastname: Barbour
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D009885:Ophthalmology / Q000379:methods*; D014054:Tomography / Q000379:methods*