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Reducing the Computational Complexity of Image Processing Using Wavelet Transform Based on the Winograd Method

  • MATHEMATICAL THEORY OF IMAGES AND SIGNALS REPRESENTING, PROCESSING, ANALYSIS, RECOGNITION AND UNDERSTANDING
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Abstract

Modern computer technology devices do not keep pace with the high growth rate of quantitative and qualitative characteristics of digital images. The computational complexity of the wavelet transform must be reduced for the hardware-friendly implementation of wavelet image processing methods on microelectronic devices. This paper proposes a new approach to reduce the computational complexity of wavelet image processing based on the Winograd method. Group pixel processing using Winograd method reduces the asymptotic computational complexity by up to 72.9% compared to the traditional pixel-by-pixel processing approach, according to the results obtained. A theoretical evaluation of the resource costs of a wavelet image processing device based on the unit-gate model showed that Winograd method reduces device delay to 73.62% and device area to 34.03% compared to the direct implementation. The greatest reduction in resource costs is observed mainly when obtaining fragments of the processed image with 5 pixels. At the same time, the greatest rate of resource reduction is observed when obtaining fragments of the processed image with 3 pixels. Further increase in the fragments size leads to a significantly smaller reduction in resource costs while increasing the complexity of circuits design. Separation of filters into several components is more hardware-friendly when using high-order wavelets. Verification of all obtained results on field-programmable gate arrays and application-specific integrated circuits is a promising direction for further research.

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ACKNOWLEDGMENTS

The authors express gratitude to the North-Caucasus Center for Mathematical Research for providing the material and technical base.

Funding

The research in section 3 was supported by the Russian Science Foundation (project no. 22-71-00009). The research in the remaining sections was supported by the Russian Science Foundation (project no. 21-71-00017).

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Authors and Affiliations

  1. North-Caucasus Federal University, 355017, Stavropol, Russian Federation

    P. A. Lyakhov, N. N. Nagornov, N. F. Semyonova & A. S. Abdulsalyamova

Authors
  1. P. A. Lyakhov
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  2. N. N. Nagornov
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  3. N. F. Semyonova
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  4. A. S. Abdulsalyamova
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Corresponding authors

Correspondence to P. A. Lyakhov, N. N. Nagornov, N. F. Semyonova or A. S. Abdulsalyamova.

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This article is a completely original work of its authors; it has not been published before and will not be sent to other publications until the PRIA Editorial Board decides not to accept it for publication.

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Additional information

Pavel Alekseyevich Lyakhov. Born 1988. Graduated from Stavropol State University, specialty “Mathematics” in 2009. Candidate of Physical and Mathematical Sciences. Head of the Department of Mathematical Modeling, North-Caucasus Federal University, Head of the Department of Modular Computing and Artificial Intelligence, regional scientific and educational mathematical center “North-Caucasus Center for Mathematical Research”. Research interests are digital signal and image processing, artificial intelligence, neural networks, modular arithmetic, parallel computing, high-performance computing, digital circuits and hardware accelerators. Author of more than 200 publications.

Nikolay Nikolaevich Nagornov. Born 1992. Graduated from North-Caucasus Federal University, specialty “Applied Mathematics and Computer Science” in 2014. Candidate of Computer Sciences. Associate Professor of the Department of Mathematical Modeling, North-Caucasus Federal University. Research interests are digital image processing, modular arithmetic, parallel computing, high-performance computing, digital circuits and hardware accelerators. Author of more than 30 publications.

Nataliya Fedorovna Semyonova. Born 1951. Graduated from the Faculty of Physics and Mathematics of the Stavropol State Pedagogical Institute in 1972. Candidate of Physical and Mathematical Sciences. Associate Professor of the Department of Mathematical Modeling, North-Caucasus Federal University. Research interests are mathematical modeling, parallel computing, residue number system, modular arithmetic, diagonal function. Author of more than 60 publications.

Albina Shikhaevna Abdulsalyamova. Born 2000. Graduated from North-Caucasus Federal University, specialty “Mathematics and Computer Science” in 2022. Laboratory assistant of the Department of Modular Computing and Artificial Intelligence, regional scientific and educational mathematical center “North-Caucasus Center for Mathematical Research”. Research interests are digital image processing, computational complexity, high-performance computing and digital circuits.

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Lyakhov, P.A., Nagornov, N.N., Semyonova, N.F. et al. Reducing the Computational Complexity of Image Processing Using Wavelet Transform Based on the Winograd Method. Pattern Recognit. Image Anal. 33, 184–191 (2023). https://doi.org/10.1134/S1054661823020074

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