The use of discrete dyadic wavelets in image processing
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 57-66.

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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.
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Yu. A. Farkov; S. A. Stroganov. The use of discrete dyadic wavelets in image processing. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 57-66. http://geodesic.mathdoc.fr/item/IVM_2011_7_a6/

[1] Lang W. C., “Wavelet analysis on the Cantor dyadic group”, Houston J. Math., 24:3 (1998), 533–544 | MR | Zbl

[2] Farkov Yu. A., “Ortogonalnye veivlety s kompaktnymi nositelyami na lokalno kompaktnykh abelevykh gruppakh”, Izv. RAN. Ser. matem., 69:3 (2005), 193–220 | MR | Zbl

[3] Farkov Yu. A., “On wavelets related to the Walsh series”, J. Approx. Theory, 161:1 (2009), 259–279 | DOI | MR | Zbl

[4] Rodionov E. A., Farkov Yu. A., “Otsenki gladkosti diadicheskikh ortogonalnykh vspleskov tipa Dobeshi”, Matem. zametki, 86:3 (2009), 429–444 | MR | Zbl

[5] Farkov Yu. A., “Biortogonalnye vspleski na gruppakh Vilenkina”, Tr. matem. in-ta im. V. A. Steklova, 265, 2009, 110–124 | MR | Zbl

[6] Schipp F., Wade W. R., Simon P., Walsh series: an introduction to dyadic harmonic analysis, Adam Hilger, N.Y., 1990 | MR | Zbl

[7] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha: teoriya i primeneniya, Izd-vo LKI, M., 2008

[8] Zalmanzon L. A., Preobrazovaniya Fure, Uolsha, Khaara i ikh primenenie v upravlenii, svyazi i drugikh oblastyakh, Nauka, M., 1983 | MR

[9] Freizer M., Vvedenie v veivlety v svete lineinoi algebry, BINOM. Laboratoriya znanii, M., 2008

[10] Broughton S. A., Bryan K. M., Discrete Fourier analysis and wavelets. Applications to signal and image processing, John Wiley Sons, Hoboken, NJ, 2009 | MR | Zbl

[11] Dobeshi I., Desyat lektsii po veivletam, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001

[12] Novikov I. Ya., Protasov V. Yu., Skopina M. A., Teoriya vspleskov, Fizmatlit, M., 2006 | MR

[13] Malozemov V. N., Masharskii S. M., “Obobschennye veivletnye bazisy, svyazannye s diskretnym preobrazovaniem Vilenkina–Krestensona”, Algebra i analiz, 13:1 (2001), 111–157 | MR | Zbl

[14] Malla S., Veivlety v obrabotke signalov, Mir, M., 2005

[15] Uelstid S., Fraktaly i veivlety dlya szhatiya izobrazhenii v deistvii, Izd-vo Triumf, M., 2003

[16] Hereford J., Roach D. W., Pigford R., “Image compression using parameterized wavelets with feedback”, Independent Component Analysis, Wavelets and Neural Networks, Proc. SPIE, 5102, 2003, 267–277

[17] Holland J. H., Adaptation in natural and artificial systems. An introductory analysis with applications to biology, control, and artificial intelligence, University of Michigan Press, Ann Arbor, 1975 | MR