Strang and Nguyen's text, Wavelets and Filter Banks, is by far
best introduction to wavelets that I have seen. The explanations of
difficult topics are informal and very approachable, yet rigor is not
sacrificed in the process. In addition to doing an excellent job of
covering the basics, the text provides very useful reviews of recent
results on a number of more special-purpose topics, including boundary
filters and lifting.
One of the nicest things about the text is that it achieves a balance
between the language of engineers and the language of mathematicians,
and it presents material in a manner that is accessible to people with a
wide range of backgrounds. My current graduate seminar on wavelets is
attended by graduate students, some advanced undergraduates, and several
professors. The members of the class come from the math department, the
computer science department, the engineering school, and the business
school. All seem to have found the book useful.
I have been extremely pleased with the book overall and give it an