Fast deconvolution with approximated PSF by RSTLS with antireflective boundary conditions

The problem of reconstructing signals and images from degraded ones is considered in this paper. The latter problem is formulated as a linear system whose coefficient matrix models the unknown point spread function and the right hand side represents the observed image. Moreover, the coefficient matrix is very ill-conditioned, requiring an additional regularization term. Different boundary conditions can be proposed. In this paper antireflective boundary conditions are considered. Since both sides of the linear system have uncertainties and the coefficient matrix is highly structured, the Regularized Structured Total Least Squares approach seems to be themore appropriate one to compute an approximation of the true signal/image.With the latter approach the original problem is formulated as an highly nonconvex one, and seldom can the globalminimumbe computed. It is shown that Regularized Structured Total Least Squares problems for antireflective boundary conditions canbedecomposed into single variable subproblemsby adiscrete sine transform. Such subproblems are then transformed into one-dimensional unimodal realvalued minimization problems which can be solved globally. Some numerical examples show the effectiveness of the proposed approach. © 2012 Elsevier B.V. All rights reserved.