Approximation by Multivariate Generalized Sampling Kantorovich Operator in the Setting of Orlicz Spaces

In this paper we study a linear 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). We alos 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 are included.