Abstract

The problem of reconstructing signals and images from degraded ones is consideredin this paper. The latter problem is formulated as a linear system whose coefficientmatrix models the unknown point spread function and the right hand side representsthe observed image. Moreover, the coefficient matrix is very ill-conditioned, requiringan additional regularization term. Different boundary conditions can be proposed. In thispaper antireflective boundary conditions are considered. Since both sides of the linearsystem have uncertainties and the coefficient matrix is highly structured, the RegularizedStructured Total Least Squares approach seems to be the more appropriate one to computean approximation of the true signal/image. With the latter approach the original problem isformulated as an highly nonconvex one, and seldom can the global minimum be computed.It is shown that Regularized Structured Total Least Squares problems for antireflectiveboundary conditions can be decomposed into single variable subproblems by a discrete sinetransform. Such subproblems are then transformed into one-dimensional unimodal realvaluedminimization problems which can be solved globally. Some numerical examplesshow the effectiveness of the proposed approach.

Autore Pugliese

• Mastronardi Nicola

Tutti gli autori

• Donatelli M.; Mastronardi N.

Titolo volume/Rivista

Journal of computational and applied mathematics

Anno di pubblicazione

2012

ISSN

0377-0427

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

Non Disponibile

Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

Non Disponibile