Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 751&ndash770;

CONVERGENCE IN VARIATION FOR THE MULTIDIMENSIONAL GENERALIZED SAMPLING SERIES AND APPLICATIONS TO SMOOTHING FOR DIGITAL IMAGE PROCESSING

Laura Angeloni, Danilo Costarelli and Gianluca Vinti

University of Perugia, Department of Mathematics and Computer Science
Via Vanvitelli 1, 06123, Perugia, Italy; laura.angeloni 'at' unipg.it

University of Perugia, Department of Mathematics and Computer Science
Via Vanvitelli 1, 06123, Perugia, Italy; danilo.costarelli 'at' unipg.it

University of Perugia, Department of Mathematics and Computer Science
Via Vanvitelli 1, 06123, Perugia, Italy; gianluca.vinti 'at' unipg.it

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.

2010 Mathematics Subject Classification: Primary 41A30, 41A05.

Key words: Convergence in variation, multidimensional generalized sampling series, sampling-Kantorovich operators, variation diminishing type property, smoothing in digital image processing.

Reference to this article: L. Angeloni, D. Costarelli and G. Vinti: Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing. Ann. Acad. Sci. Fenn. Math. 45 (2020), 751–770.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4532