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

Abstract

In this article, 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 L ϕ(ℝ n ) that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in L p (ℝ n )-spaces, L αlog β L(ℝ n )-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and image processing applications are included.