In a regularized approach to Poisson data inversion, the problem is reduced to the minimization of an objective function which consists of two terms: a data fidelity function, related to a generalized Kullback-Leibler divergence, and a regularization function expressing a priori information on the unknown image. This second function is multiplied by a parameter β, sometimes called regularization parameter, which must be suitably estimated for obtaining a sensible solution. In order to estimate this parameter, a discrepancy principle has been recently proposed, that implies the minimization of the objective function for several values of β. Since this approach can be computationally expensive, it has also been proposed to replace it with a constrained minimization, the constraint being derived from the discrepancy principle. In this paper we intend to compare the two approaches from the computational point of view. In particular, we propose a secant-based method for solving the discrepancy equation arising in the first approach; when this root finding algorithm can be combined with an efficient solver of the inner minimization problems, the first approach can be competitive and sometimes faster than the second one.

Numerical Methods for Parameter Estimation in Poisson Data Inversion / Zanni, Luca; Benfenati, Alessandro; Bertero, Mario; Ruggiero, Valeria. - In: JOURNAL OF MATHEMATICAL IMAGING AND VISION. - ISSN 0924-9907. - STAMPA. - 52:3(2015), pp. 397-413. [10.1007/s10851-014-0553-9]

Numerical Methods for Parameter Estimation in Poisson Data Inversion

ZANNI, Luca;
2015

Abstract

In a regularized approach to Poisson data inversion, the problem is reduced to the minimization of an objective function which consists of two terms: a data fidelity function, related to a generalized Kullback-Leibler divergence, and a regularization function expressing a priori information on the unknown image. This second function is multiplied by a parameter β, sometimes called regularization parameter, which must be suitably estimated for obtaining a sensible solution. In order to estimate this parameter, a discrepancy principle has been recently proposed, that implies the minimization of the objective function for several values of β. Since this approach can be computationally expensive, it has also been proposed to replace it with a constrained minimization, the constraint being derived from the discrepancy principle. In this paper we intend to compare the two approaches from the computational point of view. In particular, we propose a secant-based method for solving the discrepancy equation arising in the first approach; when this root finding algorithm can be combined with an efficient solver of the inner minimization problems, the first approach can be competitive and sometimes faster than the second one.
2015
52
3
397
413
Numerical Methods for Parameter Estimation in Poisson Data Inversion / Zanni, Luca; Benfenati, Alessandro; Bertero, Mario; Ruggiero, Valeria. - In: JOURNAL OF MATHEMATICAL IMAGING AND VISION. - ISSN 0924-9907. - STAMPA. - 52:3(2015), pp. 397-413. [10.1007/s10851-014-0553-9]
Zanni, Luca; Benfenati, Alessandro; Bertero, Mario; Ruggiero, Valeria
File in questo prodotto:
File Dimensione Formato  
VOR_Numerical Methods for Parameter.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 1.1 MB
Formato Adobe PDF
1.1 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1062254
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 19
social impact