On a novel probabilistic Sampling Kantorovich operators and their application

TL;DR

This paper introduces a new probabilistic sampling Kantorovich operator, establishing its theoretical foundations, demonstrating its application to image processing, and comparing its performance with classical methods using metrics like PSNR and SSIM.

Contribution

The paper develops a novel probabilistic sampling Kantorovich operator and provides theoretical proofs, numerical examples, and a comparative analysis with classical operators.

Findings

The PSK-operators are effective in image processing tasks.

Numerical examples demonstrate the operator's convergence and features.

Comparative analysis shows improved metrics over classical operators.

Abstract

This article starts with the fundamental theory of stochastic type convergence and the significance of uniform integrability in the context of expectation value. A novel probabilistic sampling kantorovich (PSK-operators) is established with the help of classical sampling operators (SK-operators). We establish the proof of the fundamental theorem of approximation and a lemma corresponding to the PSK- operators. Moreover, some examples are illustrated not only in numerical form but also in a detailed study of some important features of an image at different samples. Eventually, a comparative analysis is made on the basis of some parameters like peak signal noise ratio (PSNR), structural similarity index (SSIM) etc. between the classical and probabilistic sense in tabulated form, which connects the whole dots of the theory present in the article.