# Regularized Total Least–Squares Approach for Nonconvolutional Linear Inverse Problems

### W. Zhu *et al.* (1999)

#### Summary

In this correspondence, a solution is developed for the regularized total least squares (RTLS)
estimate in linear inverse problems where the linear operator in nonconvolutional. Our approach
is based on a Rayleigh quotient (RQ) formulation of the TLS problem, and we accomplish
regularization by modifying the RQ function to enforce a smooth solution. A conjugate gradient
algorithm is used to minimize the modified RQ function. As an example, the proposed approach has
been applied to the perturbation equation encountered in optical tomography. Simulation results
show that this method provides more stable and accurate solutions than the regularized least
squares and a previously reported total least squares approach, also based on the RQ
formulation.