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Titolo/Abstract/Parole chiave

A discrepancy principle for Poisson data: uniqueness of the solution for 2D and 3D data

Bonettini, Silvia - Ruggiero, Valeria (2010) A discrepancy principle for Poisson data: uniqueness of the solution for 2D and 3D data. [Preprint] (Inedito)

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    Abstract

    This paper is concerned with the uniqueness of the solution of a nonlinear equation, named discrepancy equation. For the restoration problem of data corrupted by Poisson noise, we have to minimize an objective function that combines a data-fidelity function, given by the generalized Kullback–Leibler divergence, and a regularization penalty function. Bertero et al. recently proposed to use the solution of the discrepancy equation as a convenient value for the regularization parameter. Furthermore they devised suitable conditions to assure the uniqueness of this solution for several regularization functions in 1D denoising and deblurring problems. The aim of this paper is to generalize this uniqueness result to 2D and 3D problems for several penalty functions, such as an edge preserving functional, a simple case of the class of Markov Random Field (MRF) regularization functionals and the classical Tikhonov regularization.

    Tipologia del documento:Preprint
    Data:9 Giugno 2010
    Istituzione:Università degli studi di Ferrara
    Struttura:Dipartimento > Matematica
    Soggetti:Area 01 - Scienze matematiche e informatiche > MAT/08 Analisi numerica
    Numero identificativo:368
    Depositato il:13 Lug 2010 10:30

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