Abstract
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 the more 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 global minimum be computed.
It is shown that Regularized Structured Total Least Squares problems for antireflective
boundary conditions can be decomposed into single variable subproblems by a discrete 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.
Anno
2012
Autori IAC
Tipo pubblicazione
Altri Autori
Donatelli Marco; Mastronardi Nicola
Editore
Koninklijke Vlaamse Ingenieursvereniging
Rivista
Journal of computational and applied mathematics