Data di Pubblicazione:
2015
Citazione:
Numerical Methods for Parameter Estimation in Poisson Data Inversion / L. Zanni, A. Benfenati, M. Bertero, V. Ruggiero. - In: JOURNAL OF MATHEMATICAL IMAGING AND VISION. - ISSN 0924-9907. - 52:3 Special Issue(2015 Jul), pp. 397-413. [10.1007/s10851-014-0553-9]
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 , 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 . 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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Poisson noise; Regularization parameter estimation; Discrepancy principle; Hypersurface regularization; Seminorm regularization
Elenco autori:
L. Zanni, A. Benfenati, M. Bertero, V. Ruggiero
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