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Kautský, Jaroslav
An algebraic construction of discrete wavelet transforms. (English). Applications of Mathematics, vol. 38 (1993), issue 3, pp. 169-193
MSC: 15A04, 42C15, 65F25, 65F30, 65T99 | MR 1218024 | Zbl 0782.65061 | DOI: 10.21136/AM.1993.104545
Keywords:
orthogonal transform; wavelet; pyramidal algorithm; discrete wavelets; banded orthogonal matrices; orthogonal wavelets; signal reduction
Summary:
Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rapid signal reduction are derived.
References:
[1] I. Daubechies: Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988), 909-996. DOI 10.1002/cpa.3160410705 | MR 0951745 | Zbl 0644.42026
[2] S. Mallat: A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal, and Machine Intell. 11 (1989), 674-693. DOI 10.1109/34.192463 | Zbl 0709.94650
[3] Y. Meyer: Ondelettes et Opèrateurs. Hermann, Paris, 1990. MR 1085487 | Zbl 0745.42011
[4] G. Strang: Wavelets and dilation equations: A brief introduction. SIAM Review 31(4) (1989), 614-627. DOI 10.1137/1031128 | MR 1025484 | Zbl 0683.42030
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