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Product Description
Ingeniously relying on elementary algebra and just a smidgen of calculus, Professor Walker demonstrates how the underlying ideas behind wavelet analysis can be applied to solve significant problems in audio and image processing, as well in biology and medicine.
Nearly twice as long as the original, this new edition provides
· 104 worked examples and 222 exercises, constituting a veritable book of review material
· Two sections on biorthogonal wavelets
· A mini-course on image compression, including a tutorial on arithmetic compression
· Extensive material on image denoising, featuring a rarely covered technique for removing isolated, randomly positioned clutter
· Concise yet complete coverage of the fundamentals of time-frequency analysis, showcasing its application to audio denoising, and musical theory and synthesis
· An introduction to the multiresolution principle, a new mathematical concept in musical theory
· Expanded suggestions for research projects
· An enhanced list of references
· FAWAV: software designed by the author, which allows readers to duplicate described applications and experiment with other ideas.
To keep the book current, Professor Walker has created a supplementary website. This online repository includes ready-to-download software, and sound and image files, as well as access to many of the most important papers in the field.
From the Back Cover
Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data.
Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLABä. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned.
Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background. --This text refers to an alternate Paperback edition.
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A Haar wavelet is the simplest type of wavelet. Read the first page
Concordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews
Ch. 2: Daubechies Wavelets: While there are numerous Daubechies wavelets Walker picks the simplest and develops important concepts. Some comfort with linear algebra and matrix notation makes this chapter easy to understand. The examples in the Haar chapter are carried forward to show how the Daubechies take care of discontinuities created by the Haar wavelet. Other Daubechies wavelts are then discussed and the Coiflets are introduced along with the need for these additional wavelets. More examples and the removal of pop noise and background static is examined. Image processing is introduced along with more examples. Great stuff even if I am not particularly interested in these topics. Chapter ends with notes and references where several URL's are presented on the various aspects of wavelets.
Ch. 3: Frequency analysis: Some familiarity with Fourier transforms will make the reader comfortable here but I do not think the familiarity essential to get the gist of where Walker is leading the reader. The idea of detecting a given sub image within a larger image is where we are lead. Chapter concludes on a roll your own wavelet section and again a notes and reference section.
Ch. 4: Beyond wavelets: Wavelet packet transforms are introduced and a few of their applications to signal compression presented. The concept of a continuous wavelet transform is brought in.
Appendix A. Software for wavelet analysis. Walker presents the URL for his software and data files.
For an introductory book I gave it the 5 stars. I really found it useful in getting me into the subject and a feeling for the level of effort I need to put forward to use wavelets for my application.
I am sure that within the first 20 pages, which are easy to understand and make for a very quick read, you will begin to see the beauty of this theory and will applaud the author's exposition.
While this book does not need much more than basic linear algebra, the author does not shy away from the mathematics where necessary - he simply motivates it by providing an intuitive understanding of the equations, so it's easy to follow.
In the very first chapter, he describes the wavelet method using examples that can be worked out by hand. (This is also mentioned in another review and contributed to me buying this book. I was doing research on another wavelet book on the site when I came across this book and it's reviews.) This helps to fix and brilliantly clarify the main ideas behind the theory. Armed with this knowledge, the reader can better appreciate the more sophisticated wavelet functions. But, the basics would be firmly planted by this book. This is rarely seen in other books dealing with this thoery.
This book is great for someone who wants to learn about this topic. It also is an excellent book for those who have an advanced graduate degree in applied mathematics since it demonstrates how to truly understand complex concepts.
The discussion is motivated with real world examples such as removing noise from signals, image enhancements, etc. These are useful examples that you can relate to. There is enough in this book and the downloadable software that you may want to undertake meaningful projects yourself. That is the confidence that you get from this book.
An outstanding quality is that the book is thin. This is a strong motivating factor since it immediately sends the message that "this method can't be that hard to grasp if the book is so short." And, this subliminal message keeps your spirits up as you read this masterpiece.
Wavelets is a mathematically intensive technique, and it seems that most authors want to show how "macho" they are by shrouding the basics under a heavy cloak of complex equations. But, true "machoism" is displayed by how deftly an author can bring a difficult topic to the lay person. James Walker does this remarkably well.
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