In this paper we study the problem of the convergence in variation for the generalized sampling series based upon averaged-type kernels in the multidimensional setting. As a crucial tool, we introduce a family of operators of sampling-Kantorovich type for which we prove convergence in Lp on a subspace of Lp(RN): therefore we obtain the convergence in variation for the multidimensional generalized sampling series by means of a relation between the partial derivatives of such operators acting on an absolutely continuous function f and the sampling-Kantorovich type operators acting on the partial derivatives of f. Applications to digital image processing are also furnished.

Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing

Laura Angeloni
;
Danilo Costarelli;Gianluca Vinti
2020

Abstract

In this paper we study the problem of the convergence in variation for the generalized sampling series based upon averaged-type kernels in the multidimensional setting. As a crucial tool, we introduce a family of operators of sampling-Kantorovich type for which we prove convergence in Lp on a subspace of Lp(RN): therefore we obtain the convergence in variation for the multidimensional generalized sampling series by means of a relation between the partial derivatives of such operators acting on an absolutely continuous function f and the sampling-Kantorovich type operators acting on the partial derivatives of f. Applications to digital image processing are also furnished.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1455556
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