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Titolo/Abstract/Parole chiave

Inexact Bregman iteration with an application to Poisson data reconstruction

Benfenati, Alessandro - Ruggiero, Valeria (2013) Inexact Bregman iteration with an application to Poisson data reconstruction. [Preprint] (Sottomesso)

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    Abstract

    This work deals with the solution of image restoration problems by an iterative regularization method based on the Bregman iteration. Any iteration of this scheme requires to exactly compute the minimizer of a function. However, in some image reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these subproblems. In this paper, we propose an inexact version of the iterative procedure, where the inexactness in the inner subproblem solution is controlled by a criterion that preserves the convergence of the Bregman iteration and its features in image restoration problems. In particular, the method allows to obtain accurate reconstructions also when only an overestimation of the regularization parameter is known. The introduction of the inexactness in the iterative scheme allows to address image reconstruction problems from data corrupted by Poisson noise, exploiting the recent advances about specialized algorithms for the numerical minimization of the generalized Kullback–Leibler divergence combined with a regularization term. The results of several numerical experiments enable to evaluate

    Tipologia del documento:Preprint
    Data:26 Marzo 2013
    Istituzione:Università degli studi di Ferrara
    Struttura:Dipartimento > Matematica
    Soggetti:Area 01 - Scienze matematiche e informatiche > MAT/08 Analisi numerica
    Parole chiave:Bregman iteration, Inexact Bregman iteration, Image restoration, Regularization parameter, Poisson noise
    Numero identificativo:380
    Depositato il:03 Apr 2013 13:33

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