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arXiv · 1906.03021

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

Laura Angeloni·Danilo Costarelli·Gianluca Vinti
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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 L^p on a subspace of L^p(R^N): 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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Laura Angeloni, Danilo Costarelli, Gianluca Vinti. 2019-06-07. Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing. https://arxiv.org/abs/1906.03021

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