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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 7, Pages 57–66 (Mi ivm7698)  
This article is cited in 10 scientific papers (total in 10 papers)

The use of discrete dyadic wavelets in image processing

Yu. A. Farkov, S. A. Stroganov

Chair of Higher Mathematics and Mathematical Modeling, Russian State Geological Prospecting University, Moscow, Russia
Full-text PDF (219 kB) Citations (10)
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Abstract: In this paper, using the discrete Walsh transform, we construct orthogonal and biorthogonal wavelets for complex periodic sequences similar to those studied earlier for the Cantor group. Results of numerical experiments demonstrate the effectiveness of image processing methods based on the constructed discrete wavelets.
Keywords: dyadic wavelets, spaces of periodic sequences, Walsh functions, discrete Walsh transform, image processing.
Received: 23.03.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 7, Pages 47–55
DOI: https://doi.org/10.3103/S1066369X11070073
Bibliographic databases:
Document Type: Article
UDC: 519.677
Language: Russian
Citation: Yu. A. Farkov, S. A. Stroganov, “The use of discrete dyadic wavelets in image processing”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 7, 57–66; Russian Math. (Iz. VUZ), 55:7 (2011), 47–55
Citation in format AMSBIB
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\pages 57--66
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\jour Russian Math. (Iz. VUZ)
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  • https://www.mathnet.ru/eng/ivm7698
  • https://www.mathnet.ru/eng/ivm/y2011/i7/p57
    • This publication is cited in the following 10 articles:
    1. Yu. A. Farkov, “Freimy v analize Uolsha, matritsy Adamara i ravnomerno raspredelennye mnozhestva”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 199, VINITI RAN, M., 2021, 17–30  mathnet  crossref
    2. M. S. Bespalov, “Troichnyi diskretnyi veivletnyi bazis”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 20:3 (2020), 367–377  mathnet  crossref
    3. M. S. Bespalov, M. S. Bespalov, “Extraction of Walsh Harmonics by Linear Combinations of Dyadic Shifts”, J Math Sci, 249:6 (2020), 838  crossref
    4. Yu. A. Farkov, M. G. Robakidze, “Parseval Frames and the Discrete Walsh Transform”, Math. Notes, 106:3 (2019), 446–456  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi, Industrial and Applied Mathematics, Construction of Wavelets Through Walsh Functions, 2019, 253  crossref
    6. Siddiqi A.H., Manchanda P., “Sampling and Approximation Theorems For Wavelets and Frames on Vilenkin Group”, 2017 International Conference on Sampling Theory and Applications (Sampta), IEEE, 2017, 614–616  crossref  isi
    7. Hu Zh., Hou Ch., “Wavelet Transformation of Road Simulation Based on Fbm Fractal Characteristics”, International Conference on Electrical and Control Engineering (Icece 2015), Destech Publications, Inc, 2015, 255–260  isi
    8. Farkov Yu.A., Rodionov E.A., “on Biorthogonal Discrete Wavelet Bases”, Int. J. Wavelets Multiresolut. Inf. Process., 13:1 (2015), 1550002  crossref  isi
    9. Lukomskii S.F., “Step Refinable Functions and Orthogonal Mra on Vilenkin Groups”, J. Fourier Anal. Appl., 20:1 (2014), 42–65  crossref  isi
    10. Yu. A. Farkov, M. E. Borisov, “Periodic dyadic wavelets and coding of fractal functions”, Russian Math. (Iz. VUZ), 56:9 (2012), 46–56  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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