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The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets

✍ Scribed by Wim Sweldens

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 274 KB
Volume: 3
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.1996.0015

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✦ Synopsis

We present the lifting scheme, a new idea for constructing compactly supported wavelets with compactly supported duals. The lifting scheme uses a simple relationship between all multiresolution analyses with the same scaling function. It isolates the degrees of freedom remaining after fixing the biorthogonality relations. Then one has full control over these degrees of freedom to custom design the wavelet for a particular application. The lifting scheme can also speed up the fast wavelet transform. We illustrate the use of the lifting scheme in the construction of wavelets with interpolating scaling functions.

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