Wavelets : A Tutorial in Theory and Applications

Rating:
Summary: Slightly outdated but solid book - more theory than apps
Review: As the title indicates, this book has some good, solid papers on wavelets/wavelet analysis. The title is a bit misleading -- the book is very theoretical and few of the papers address how wavelet techniques can be used to solve scientific and engineering problems. This is not to say that the book is not valuable -- it is edited by Chui, an extremely successful organizer of conferences, who has extensive experience writing and editing very good books. It is a mathematician's book.

At the time of its publication, this book was one of the better applications books, the other two comparable applications books were edited by: (1) Combes et al. (2) Ruskai et al.. This book has many more references to relevant works than the Combes and Ruskai books.

Unfortunately, 8 years have passed since the publication of this book, and a lot of progress takes place in the field of wavelets. Some techniques which looked promising 8 years ago did not live up to expectations, and some new ideas with very practical applications are not addressed in this book. This second remark may not be entirely fair since applications of wavelets have become so widespread that it would be impossible for any one book to cover all.

This book does not contain problems to assign for homework. It might be appropriate to use some chapters in the book for supplementary reading. in a graduate course or in an upper division special topics course. Unfortunately, the price is a bit high to make it required reading as a supplementary text for a course.

Some of the the theoretical papers, particularly the first 3 in Section I would not be of interest to applications oriented people since no work has followed from these papers. They are very specialized theoretical works.The papers in Section II cover topics which have become a standard tools in wavelet analysis, e.g., splines, biorthogonal wavelets, multiresolution analysis (MRA).Papers in Section III are a bit outdated. There was a period when wavelets were hyped and people in the research community believed that they could lead to improvements in the solution of PDEs. Unfortunately, few new practical tools have emerged. Only the paper on MRA in section IV may be of interest to a wide audience, but it too is rather theoretical. Sections V VI and VII were intended to cover applications to digital signal processing (DSP). If the primary interest of a reader is DSP, this is the wrong book to purchase in this day and age. Mallat's book: a Wavelet Tour of Signal Processing is far more comprehensive and up-to-date.