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

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-08-13 DOI:10.1002/mma.70025

Metin Turgay, Tuncer Acar

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引用次数: 0

Abstract

In this paper, we introduce bivariate modified sampling Kantorovich operators, which extend the classical sampling Kantorovich operators by incorporating a transformation function $ρ$ . 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 $ρ$ . Moreover, we study modular convergence of these operators in Orlicz spaces $L^{η} (ℝ^{2})$ . Finally, we present some $ρ$ -kernels and applications to image processing. The newly constructed operators present better process and higher PSNR value for some parameters $w$ and function $ρ$ .

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二元采样Kantorovich算子的新推广及其在图像处理中的应用

本文引入了二元修正采样Kantorovich算子，该算子通过引入变换函数ρ $$ \rho $$扩展了经典采样Kantorovich算子。本文首先给出了基本定义，包括引入了新的二元加权连续模，以及它的基本性质。从连续函数空间的点向收敛和一致收敛的角度研究了新构造的算子。研究了由ρ $$ \rho $$构造的函数的加权空间中算子族的加权逼近性质。而且，研究了这些算子在Orlicz空间中的模收敛性2 . $$ {L}&#x0005E;{\eta}\left({\mathbb{R}}&#x0005E;2\right) $$。最后，我们介绍了一些ρ $$ \rho $$ -核及其在图像处理中的应用。对于一些参数w $$ w $$和函数ρ $$ \rho $$，新构造的算子表现出更好的处理过程和更高的PSNR值。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.