Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing
Functional Analysis
2019-06-10 v1
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.
Cite
@article{arxiv.1906.03021,
title = {Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing},
author = {Laura Angeloni and Danilo Costarelli and Gianluca Vinti},
journal= {arXiv preprint arXiv:1906.03021},
year = {2019}
}