Geodesic
New generalization of orthogonal wavelet bases
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 264-271
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Wavelet bases are constructed for $n$ scaling functions. Fast algorithms for computing coefficients of expanding a function over such bases are presented.
Keywords: multiresolution analysis, wavelets, scaling functions. 
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E. A. Pleshcheva. New generalization of orthogonal wavelet bases. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 264-271. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a24/

[1] Novikov I.Ya., Protasov V.Yu., Skopina M.A., Teoriya vspleskov, Fizmatlit, M., 2005, 616 pp.

[2] Berkolaiko M.Z., Novikov I.Ya., “O beskonechno gladkikh pochti-vspleskakh s kompaktnym nositelem”, Dokl. RAN, 326:6 (1992), 935–938 | Zbl

[3] de Boor C., DeVore R., Ron A., “On the construction of multivariate (pre) wavelets”, Constr. Approx., 9 (1993), 123–166 | DOI | MR | Zbl

[4] Strela V., “Multiwavelets: regularity, orthogonality and symmetry via two-scale similarity transform”, Stud. Appl. Math., 98:4 (1997), 335–354 | DOI | MR | Zbl

[5] Strela V., Heller P.N., Strang G., Topivala P., Heil C., “The application of multiwavelet filterbanks to image processing”, IEEE Trans. Signal Processing, 8:4 (1999), 548–563

[6] Strang G., Strela V., “Short wavelets and matrix dilation equations”, IEEE Trans. Signal Processing, 43:1 (1995), 108–115 | DOI

[7] Plescheva E.A., “KMA-podobnye posledovatelnosti podprostranstv $L^2(\mathbb R)$ v sluchae dvukh masshtabiruyuschikh funktsii.”, Tr. 40-i Vseros. molodezh. konf. “Problemy teoreticheskoi i prikladnoi matematiki”, Ekaterinburg, 2009, 88–92

[8] Dobeshi I., Desyat lektsii po veivletam, Dinamika, M.; Izhevsk, 2001, 464 pp.

[9] Novikov I.Ya., Stechkin S.B., “Osnovy teorii vspleskov”, Uspekhi mat. nauk, 53:6(324) (1998), 53–128 | Zbl

[10] Petukhov A.P., Vvedenie v teoriyu bazisov vspleskov, Izd-vo SPbGTU, SPb., 1999, 132 pp.

[11] Mallat S., “Multiresolution approximation and wavelet orthonormal bases of $L^2(\mathbb R)$”, Trans. AMS, 315 (1989), 69–87 | MR | Zbl