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 the exact computation of 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 us 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 us 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 us to evaluate the proposed scheme for image deblurring or denoising in the presence of Poisson noise.

Inexact Bregman iteration with an application to Poisson data reconstruction / A. Benfenati, V. Ruggiero. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 29:6(2013), pp. 065016.1-065016.31. [10.1088/0266-5611/29/6/065016]

Inexact Bregman iteration with an application to Poisson data reconstruction

A. Benfenati
;
2013

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 the exact computation of 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 us 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 us 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 us to evaluate the proposed scheme for image deblurring or denoising in the presence of Poisson noise.
Settore MAT/08 - Analisi Numerica
Article (author)
File in questo prodotto:
File Dimensione Formato  
pdf.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 1.37 MB
Formato Adobe PDF
1.37 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/657524
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 17
social impact