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Framelets: MRA-based constructions of wavelet frames

✍ Scribed by Ingrid Daubechies; Bin Han; Amos Ron; Zuowei Shen

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 453 KB
Volume: 14
Category: Article
ISSN: 1063-5203
DOI: 10.1016/s1063-5203(02)00511-0

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✦ Synopsis

We discuss wavelet frames constructed via multiresolution analysis (MRA), with emphasis on tight wavelet frames. In particular, we establish general principles and specific algorithms for constructing framelets and tight framelets, and we show how they can be used for systematic constructions of spline, pseudo-spline tight frames, and symmetric bi-frames with short supports and high approximation orders. Several explicit examples are discussed. The connection of these frames with multiresolution analysis guarantees the existence of fast implementation algorithms, which we discuss briefly as well.

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