Construction of orthogonal multiwavelet bases
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 221-230
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We propose a method for constructing orthogonal multiwavelet bases of the space $\mathbf L^2(\mathbb R)$ for any known multiscaling functions that generate a multiresolution analysis of dimension greater than 1.
Keywords: multiwavelet, multiresolution analysis, multiscaling function, mask, matrix mask.
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E. A. Pleshcheva; N. I. Chernykh. Construction of orthogonal multiwavelet bases. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 221-230. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a20/

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

[2] Keinert F., Wavelets and multiwavelets, Studies in advanced mathematics, 42, Chapman Hall/CRC Press, Boca Raton, 2003, 275 pp. | MR

[3] Lawton W., Lee S., Shen Z., “An algorithm for matrix extension and wavelet construction”, Math. Comp., 65:214 (1996), 723–737 | DOI | MR | Zbl

[4] Scopina M., “On construction of multivariate wavelet frames”, Applied and Computational Harmonic Analysis, 27:1 (2009), 55–72 | DOI | MR

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

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

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