"D. Walnut's lovely book aims at the upper undergraduate level,
and so it includes relatively more preliminary material . . . than
is typically the case in a graduate text. It goes from Haar systems
to multiresolutions, and then the discrete wavelet transform . . .
The applications to image compression are wonderful, and the best I
have seen in books at this level. I also found the analysis of the
best choice of basis, and wavelet packet, especially attractive.
The later chapters include MATLAB codes. Highly recommended "
Bulletin of the AMS
An Introduction to Wavelet Analysis provides a comprehensive
presentation of the conceptual basis of wavelet analysis, including
the construction and application of wavelet bases.
The book develops the basic theory of wavelet bases and
transforms without assuming any knowledge of Lebesgue integration
or the theory of abstract Hilbert spaces. The book elucidates the
central ideas of wavelet theory by offering a detailed exposition
of the Haar series, and then shows how a more abstract approach
allows one to generalize and improve upon the Haar series. Once
these ideas have been established and explored, variations and
extensions of Haar construction are presented. The mathematical
prerequisites for the book are a course in advanced calculus,
familiarity with the language of formal mathematical proofs, and
basic linear algebra concepts.
Features:
* Rigorous proofs with consistent assumptions about the
mathematical background of the reader (does not assume familiarity
with Hilbert spaces or Lebesgue measure).
* Complete background material on is offered on Fourier analysis
topics.
* Wavelets are presented first on the continuous domain and
later restricted to the discrete domain for improved motivation and
understanding of discrete wavelet transforms and applications.
* Special appendix, "Excursions in Wavelet Theory, " provides a
guide to current literature on the topic.
* Over 170 exercises guide the reader through the text.
An Introduction to Wavelet Analysis is an ideal text/reference
for a broad audience of advanced students and researchers in
applied mathematics, electrical engineering, computational science,
and physical sciences. It is also suitable as a self-study
reference guide for professionals."
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