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John Sasso, Jr., Rensselaer Polytechnic Institute, Troy, NY
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PostPosted: Fri Nov 29, 2002 2:22 pm    
Subject: Question
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Question


As part of my research (on the mathematics side) I managed to show, in
considerable detail, how an orthonormal wavelet basis

psi(t) = sqrt(2)*SUM{(-1)^k*h[1-k]*phi(2t-k)}

is derived from a multireolutional analysis (which is orthogonal).
(I'd like to thank Chris Brislawn & I.G. Rosen, from Los Alamos Lab, for
their report - which helped out considerably). From this derivation, I have
a much greater understanding of multiresolution analysis and how one is
able to derive orthonormal wavelet bases from it (I plan to submit a full
report to the math dept. here).

Now, I have another hurdle to overcome - the regularity and approximation
properties of orthonormal wavelet bases. I have some understanding of the
concept behind vanishing moments and its connection to the degree to which
the associated wavelet basis approximates a function. However, the math
behind vanishing moments appears very complicated (I have a background
in real analysis and introductory functional analysis). Nonetheless, I
have to go about and describe, in considerable detail, the connection between
vanishing moments and its correspondence with wavelets. So my question is:
can anyone provide me with any references (wavelet-related or not) that
which describe vanishing moments, in a rather "readable" format? The
report I intend to present to the math dept. is intended to be easy-to-
follow, but neglects none of the mathematics involved (I'm still dealing with
mathematicians, but the intended audience is seniors and grads). Any help
on this (difficult) matter of vanishing moments & wavelets would be
very much appreciated!

Thank-you very much, -- John

John Sasso, Jr.
Rensselaer Polytechnic Institute, Troy, NY
Senior, Computer Science '93
E-mail: sassoj@rpi.edu
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