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Title: An algebraic construction of discrete wavelet transforms (English)
Author: Kautský, Jaroslav
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 38
Issue: 3
Year: 1993
Pages: 169-193
Summary lang: English
Category: math
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. (English)
Keyword: orthogonal transform
Keyword: wavelet
Keyword: pyramidal algorithm
Keyword: discrete wavelets
Keyword: banded orthogonal matrices
Keyword: orthogonal wavelets
Keyword: signal reduction
MSC: 15A04
MSC: 42C15
MSC: 65F25
MSC: 65F30
MSC: 65T99
idZBL: Zbl 0782.65061
idMR: MR1218024
DOI: 10.21136/AM.1993.104545
Date available: 2008-05-20T18:45:27Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] I. Daubechies: Orthonormal bases of compactly supported wavelets.Comm. Pure Appl. Math. 41 (1988), 909-996. Zbl 0644.42026, MR 0951745, 10.1002/cpa.3160410705
Reference: [2] S. Mallat: A theory for multiresolution signal decomposition: The wavelet representation.IEEE Trans. Pattern Anal, and Machine Intell. 11 (1989), 674-693. Zbl 0709.94650, 10.1109/34.192463
Reference: [3] Y. Meyer: Ondelettes et Opèrateurs.Hermann, Paris, 1990. Zbl 0745.42011, MR 1085487
Reference: [4] G. Strang: Wavelets and dilation equations: A brief introduction.SIAM Review 31(4) (1989), 614-627. Zbl 0683.42030, MR 1025484, 10.1137/1031128


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