We propose a method, called ACQUIRE, for the solution of constrained optimization prob- lems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback–Leibler divergence term and a TV regularizer, sub- ject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback–Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole se- quence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality.

di Serafino, D., Landi, G., Viola, M. (2020). ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration. APPLIED MATHEMATICS AND COMPUTATION, 364, 1-23 [10.1016/j.amc.2019.124678].

ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration

Landi, Germana;
2020

Abstract

We propose a method, called ACQUIRE, for the solution of constrained optimization prob- lems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback–Leibler divergence term and a TV regularizer, sub- ject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback–Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole se- quence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality.
2020
di Serafino, D., Landi, G., Viola, M. (2020). ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration. APPLIED MATHEMATICS AND COMPUTATION, 364, 1-23 [10.1016/j.amc.2019.124678].
di Serafino, Daniela; Landi, Germana; Viola, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/698078
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