Construction of a Parametric Family of Wavelets and Its Use in Image Processing

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Abstract

This article is devoted to the construction of a parametric family of biorthogonal wavelets according to the lifting scheme and subdivision schemes, and the use of such a family in the problem of image rendering when part of the pixel data in the image is missing or overwritten in some way. The parametric family of wavelets provides a parametric family of filters for restoring damaged images. With such a recovery, the desired wavelet is selected not from any general considerations, but from a parametric family in the process of solving an optimization problem.

General Information

Keywords: wavelet, lifting scheme, subdivision scheme, image processing

Journal rubric: Data Analysis

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2023130401

Received: 28.09.2023

Accepted:

For citation: Bityukov Y.I., Bityukov P.Y. Construction of a Parametric Family of Wavelets and Its Use in Image Processing. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2023. Vol. 13, no. 4, pp. 7–22. DOI: 10.17759/mda.2023130401. (In Russ., аbstr. in Engl.)

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Information About the Authors

Yuri I. Bityukov, Doctor of Engineering, Professor of the Department of Probability Theory and Computer Modeling, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0009-0008-6384-0564, e-mail: yib72@mail.ru

Pavel Y. Bityukov, Bachelor student, Moscow Power Engineering Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0009-0000-8697-7047, e-mail: p.bityukoff@yandex.ru

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