Are there any suggestions for introductory books on wavelets? I want a book, not online material or tutorials.
In a course on Fourier Analysis, we used Fourier Analysis and Applications by Gasquet and Witomski (translated by Ryan). The subtitle is "Filtering, Numerical Computation, Wavelets". The wavelets section is one chapter at the end so it doesn't go into much detail specifically on wavelets. So if you already know a lot of Fourier analysis then I wouldn't use this book, but if you also need to know the Fourier analysis background then it's a reasonable place to start. It's quite readable as well.
- ISBN: 0-387-98485-2
- Publisher: Springer, Texts in Applied Mathematics 30
- MathSciNet: MR1657104 (includes review)
I think "Ripples in Mathematics: The Discrete Wavelet Transform" by Arne Jensen and Anders la Cour-Harbo (Springer 2001) is a masterpiece of elegant exposition. You can find it here. I learned more about wavelets from this book than from any other source.
A very gentle introduction is Boggess & Narcowich, A First Course in Wavelets with Fourier Analysis. I should warn you, though, they're pretty fast and loose with the hypotheses of their theorems. You'll be fine if you've studied advanced linear algebra, and especially fine if you already know some Fourier analysis.
There's also Mallat's A Wavelet Tour of Signal Processing: The Sparse Way. I haven't read very much of it, so I don't have a strong opinion on it yet. It's definitely more difficult than Boggess & Narcowich, but then it probably has about ten times the content (no exaggeration).