Regularized total least squares approach for nonconvolutional linear inverse problems

In this correspondence, a solution is developed for the regularized total l east squares (RTLS) estimate in linear inverse problems where the linear op erator is nonconvolutional. Our approach is based on a Rayleigh quotient (R Q) formulation of the TLS problem, and we accomplish regularization by modi fying the RQ function to enforce a smooth solution. A conjugate gradient al gorithm is used to minimize the modified RQ function. As an example, the pr oposed approach has been applied to the perturbation equation encountered i n optical tomography. Simulation results show that this method provides mor e stable and accurate solutions than the regularized least squares and a pr eviously reported total least squares approach, also based on the RQ formul ation.