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Journal of Electrical and Computer Engineering
Volume 2010, Article ID 241467, 18 pages
http://dx.doi.org/10.1155/2010/241467
Review Article

Antireflective Boundary Conditions for Deblurring Problems

Dipartimento di Fisica e Matematica, Università dell'Insubria-Sede di Como, Via Valleggio 11, 22100 Como, Italy

Received 30 June 2010; Accepted 8 July 2010

Academic Editor: Owe Axelsson

Copyright © 2010 Marco Donatelli and Stefano Serra-Capizzano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This survey paper deals with the use of antireflective boundary conditions for deblurring problems where the issues that we consider are the precision of the reconstruction when the noise is not present, the linear algebra related to these boundary conditions, the iterative and noniterative regularization solvers when the noise is considered, both from the viewpoint of the computational cost and from the viewpoint of the quality of the reconstruction. In the latter case, we consider a reblurring approach that replaces the transposition operation with correlation. For many of the considered items, the anti-reflective algebra coming from the given boundary conditions is the optimal choice. Numerical experiments corroborating the previous statement and a conclusion section end the paper.