Loop group factorization of biorthogonal wavelet bases. (English) Zbl 0974.42029
Gesztesy, Fritz (ed.) et al., Stochastic processes, physics and geometry: New interplays. II. A volume in honor of Sergio Albeverio. Proceedings of the conference on infinite dimensional (stochastic) analysis and quantum physics, Leipzig, Germany, January 18-22, 1999. Providence, RI: American Mathematical Society (AMS). CMS Conf. Proc. 29, 59-73 (2000).
Biorthogonal wavelets give rise to perfect reconstruction filters which are very useful in data compression. The authors propose a method of factorization of the corresponding polyphase matrix in factors of low computational complexity. The polyphase matrix is interpreted as a loop in \(\text{GL}(2,\mathbb{C})\). The main result of this paper is a simple algorithm for the decomposition of biorthogonal filters with finite impulse response into elementary filters.
For the entire collection see [Zbl 0953.00049].
For the entire collection see [Zbl 0953.00049].
Reviewer: Manfred Tasche (Rostock)
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 22E67 | Loop groups and related constructions, group-theoretic treatment |
| 43A80 | Analysis on other specific Lie groups |
| 94A11 | Application of orthogonal and other special functions |
