Wavelets Generated by Vector Multiresolution Analysis

✍ Scribed by Ruilin Long; Wen Chen; Shenglan Yuan

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 437 KB
• Volume: 4
• Category: Article
• ISSN: 1063-5203
• DOI: 10.1006/acha.1997.0216

✦ Synopsis

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 Å 1) and Long-Chen (d § 1). Roughly speaking, to get a biorthogonal vector-MRA from a given couple {H 0 (j); H ˜0(j)} of trigonometric polynomial matrices satisfying ͚ n H 0 (j / np)H H * 0 (j / np) Å I m (modulo some other natural mild conditions), it is needed only to check if both of the spectral radius of the transition operators P H 0 , and P H H 0 restricted on some suitable invariant space P 0 , are less than 1.