In this paper we study a nonlinear version of the Sampling Kantorovich type operators in a multivariate setting and we show applications to Image Processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces $\Lphi$ that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in $L^p(\R^n)$-spaces, $L^{\alpha}\log^{\beta}L(\R^n)$-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and Image Processing applications are included.

Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing

COSTARELLI, Danilo;VINTI, Gianluca
2013

Abstract

In this paper we study a nonlinear version of the Sampling Kantorovich type operators in a multivariate setting and we show applications to Image Processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces $\Lphi$ that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in $L^p(\R^n)$-spaces, $L^{\alpha}\log^{\beta}L(\R^n)$-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and Image Processing applications are included.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11391/529097
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