Fast high-resolution image reconstruction using tikhonov regularization based total least squares

The solution of an ill-conditioned total least squares (TLS) problem from highresolution imaging by the regularization approach of Golub, Hansen, and O'Leary [SIAM J. Matrix Anal. Appl., 21 (2000), pp. 185-194] is considered. This work solves the regularized TLS problem as a system of nonlinear equations in the two regularization parameters. Since the Jacobian of the system can be computed inexpensively, the approach is based upon Newton's method. From experimental results, the algorithm produces a fast computation of the solution of the high-resolution image reconstruction problem.