A New Generalization of Bivariate Sampling Kantorovich Operators and Applications to Image Processing

In this paper, we introduce bivariate modified sampling Kantorovich operators, which extend the classical sampling Kantorovich operators by incorporating a transformation function $\rho$. The paper begins by presenting essential definitions, including to introduce new bivariate weighted modulus of continuity, and its fundamental properties. The newly constructed operators are studied in terms of pointwise and uniform convergence in spaces of continuous functions. We investigate weighted approximation properties of the family of operators in weighted spaces of functions constructed by $\rho$. Moreover, we study modular convergence of these operators in Orlicz spaces $L^{\eta }\left({ℝ}^2\right)$. Finally, we present some $\rho$-kernels and applications to image processing. The newly constructed operators present better process and higher PSNR value for some parameters $w$ and function $\rho$.