𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Riesz wavelets and generalized multiresolution analyses

✍ Scribed by Marcin Bownik


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
145 KB
Volume
14
Category
Article
ISSN
1063-5203

No coin nor oath required. For personal study only.

✦ Synopsis


We investigate Riesz wavelets in the context of generalized multiresolution analysis (GMRA). In particular, we show that Zalik's class of Riesz wavelets obtained by an MRA is the same as the class of biorthogonal wavelets associated with an MRA.


πŸ“œ SIMILAR VOLUMES


Riesz Bases and Multiresolution Analyses
✍ R.A. Zalik πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 138 KB

Recently we found a family of nearly orthonormal affine Riesz bases of compact support and arbitrary degrees of smoothness, obtained by perturbing the onedimensional Haar mother wavelet using B-splines. The mother wavelets thus obtained are symmetric and given in closed form, features which are gene

Wavelets Generated by Vector Multiresolu
✍ Ruilin Long; Wen Chen; Shenglan Yuan πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 437 KB

The paper presents a general approach to the construction of so-called biorthogonal vector-MRA and its related wavelets of L 2 (R d ). The presented algorithm is very close to the one in the classical case given by Cohen-Daubechies (d Γ… 1) and Long-Chen (d Β§ 1). Roughly speaking, to get a biorthogon

Characterizations of Biorthogonal Wavele
✍ Hong Oh Kim; Rae Young Kim; Jae Kun Lim πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 130 KB

We first characterize the Riesz wavelets which are associated with multiresolution analyses (MRAs) and the Riesz wavelets whose duals are also Riesz wavelets. The characterizations show that if a Riesz wavelet is associated with an MRA, then it has a dual Riesz wavelet. We then improve Wang's charac

Adaptive multiresolution and wavelet-bas
✍ Marc Thuillard πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 162 KB

New adaptive search methods based on multiresolution analysis and wavelet theory are introduced and discussed within the framework of the Markov theory. These stochastic search methods are suited to problems for which good solutions tend to cluster within the search space. Multiresolution search met