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   -> Volume 3, Issue 4

Question: Wavelets and overcomplete representations
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John J. Sasso Jr. (

PostPosted: Mon Dec 02, 2002 12:50 pm    
Subject: Question: Wavelets and overcomplete representations
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Question: Wavelets and overcomplete representations

I have two questions...

1. Given a normalized wavelet whose set of shifts and dilates constitute
a tight frame of "redundancy factor" R, has there been any research in
the area of "extracting" an orthonormal wavelet, or orthogonal
multiresolution analysis from such a wavelet? I was musing about this idea
when looking at an example on page 181 in Daubechies' book (for a wavelet
which was the union of three shifted copies of a dilated Haar basis).

2. I've been reading some of Mallat's papers on the analysis of singularities
using wavelets, and associated properties with Holder and Lipschitz
continuity, etc... (and a mention of microlocalization theory as well).
Can anyone point me to some texts and/or articles - not necessarily
concerning wavelets - which will give me for insight into these
properties (I have found nothing on microlocalization theory, which I
believe concerns negative Lipschitz exponents)?

Any help on these matters is appreciated!

-- John
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