Max-product type multivariate sampling operators and applications to image processing

•Combining the max-product and sampling type operators using the fractional mean value of the approximated functions.•The convergence behavior of the operators in Lp spaces and a fast rate of convergence of the operators for functions that belong to the Lipschitz class.•An efficient algorithm for im...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2022-04, Vol.157, p.111914, Article 111914
Main Author: Kadak, Ugur
Format: Article
Language:English
Subjects:
Image processing
Max-product operator
Multivariate fractional calculus
Sampling operators
Signal processing
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Summary:•Combining the max-product and sampling type operators using the fractional mean value of the approximated functions.•The convergence behavior of the operators in Lp spaces and a fast rate of convergence of the operators for functions that belong to the Lipschitz class.•An efficient algorithm for image reconstruction and enhancement by the max-product sampling operators based upon various kernels.•Illustrative examples and graphs to demonstrate the convergence behavior in both one and two-dimensional cases.•The results may also be applied to fuzzy inference systems used for the image reconstruction, contrast enhancement of color images. In this work, we introduce and study a new family of max-product type multivariate sampling operators based on the fractional integral operator. We discuss some important properties, and establish the approximation behaviors of these operators in Lp spaces, for 1≤p
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2022.111914