lyall@vuvlsi.ee.vill.edu (Mike Lyall) Guest

Posted: Mon Dec 02, 2002 11:32 am Subject: Reply to Wavelet Digest 3.1:




Reply to Wavelet Digest 3.1:
Hi Suman,
I would like to offer some suggestions for you and others beginning to learn
about wavelets. I have been studying wavelets for about 6 months now,
so I've read alot of papers, books, etc., trying to learn about them.
As an engineer, you probably should concentrate on reading wavelet papers
in the engineering journals. These papers will relate to concepts that
you are already familiar with, so it will be easier to see their properties.
You should begin by learning the motivation for the wavelet transform. This
involves a comparison against the Fourier Transform and the ShortTime Fourier
Transform. I think you should begin by limiting yourself to the Discete WT only,
since it is less involved. Then, you should spend some time studying the multi
resolution analysis (MRA) introduced by Mallat. This will shed light on the
specific properties of wavelets. I also think it is important that you study
the concept of filter banks. These are well known in the signal processing
community and several excellent papers have been written. Wavelets can
be generated from filter banks, and they also relate to subband coding for
image compression, the hot area for wavelets right now.
There are many papers written on wavelets by the mathematical community.
You should wait until you master some of the basics before you tackle these.
In fact, many of the wavelet introductions are written by mathematicians. While
these are excellent papers, it is easy to get lost at first. Their motivations
are slightly different from engineering ones, and there are subtle notation
differences that can be difficult to overcome at first.
At this point, you should be able to handle most of the wavelet literature.
You can then move on to some of the books, like Ten Lectures, which is an
excellent combination on almost all of the work done in wavelets. As a matter
of fact, I would recommend reading this book *while* you are reading the
introductory topics I mentioned above. It really ties everything together well.
Now for the articles/papers/books.
The following are ones I found the most useful when I was starting out:
General Introduction/Motivations
O. Rioul and M. Vetterli, "Wavelets and Signal Processing," IEEE Signal
Processing Magazine, October 1991, pp. 1435.
Don Lancaster, "Hardware Hacker: Understanding transforms, video compression
secrets, ..., and more wavelet breakthroughs," RadioElectronics Magazine,
July 1991, pp. 68  ?.
Y. Meyer, Book Reviews, (BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL
SOCIETY, Vol. 28, No.2, April 1993), pp. 350360. Review of the books
"An introduction to wavelets", by C. Chui, and "Ten Lectures on Wavelets", by
I. Daubechies.
Multiresolution analysis
S. Mallat, "A Theory for Multiresolution Signal Decomposition: The Wavelet
Representation," IEEE Trans. on Patt. Anal. and Mach. Intell., July 1989,
pp. 674  693.
B. Jawerth and W. Sweldens, "An Overview of Wavelet Based Multiresolution
Analyses", To appear in SIAM Review, available by anonymous ftp from
maxwell.math.sc.edu as /pub/wavelet/papers/imi_reports/imi93_1.ps
Wavelets and Filter Banks
M. Vetterli and C. Herley, "Wavelets and Filter Banks: Theory and Design,"
IEEE Trans. Sig. Proc., Sept. 1992, pp. 22072232.
P.P. Vaidyanathan, "Theory and Design of MChannel Maximally Decimated
Quadrature Mirror Filters with Arbitrary M, Having the PerfectReconstruction
Property," IEEE Trans. ASSP, April 1987, pp. 476492.
M. Vetterli, "Filter Banks Allowing Perfect Reconstruction," Signal Processing,
vol. 10, no. 3, 1986, pp. 219244.
Mathematical Papers
B. Jawerth and W. Sweldens, "An Overview of Wavelet Based Multiresolution
Analyses", To appear in SIAM Review, available by anonymous ftp from
maxwell.math.sc.edu as /pub/wavelet/papers/imi_reports/imi93_1.ps
G. Strang, "Wavelets and Dilation Equations: A Brief Introduction," SIAM
Review, Dec. 1989, pp. 614627.
Books
I. Daubechies, Ten Lectures on Wavelets (CBMSNSF Series), Philadelphia:
SIAM, 1992.
Lecture Notes/Theses
Any you can get your hands on!
This is just a small list of papers and books. I am sure there are many
other excellent works out there. Hopefully, others will add to this list
so that it will be more complete.
I hope this helps. Good luck!!! 
