# An introduction to wavelets, and the wavelet transform

I am looking for a good introduction to the wavelet transform, particularly in the context of image processing. I am very comfortable with the Fourier transforms, and I've got a good background in applied math (undergraduate physics degree, masters in optics, and significant professional experience in image processing and various other number crunching tasks).

Unfortunately, I haven't been able to find an introduction to the topic that suits me. There is a lot of literature on the topic in a pure math context, which I can handle if I need to but not in a time-efficient manner. Other references are more applied, but either assume existing knowledge of wavelets, or fail to give any mathematical background whatsoever, and skip directly to "cookbook" style descriptions of wavelet applications, such as image compression.

Can anybody recommend some references that would help me?

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Tried Mallat? – J. M. Apr 20 '11 at 4:46
@J.M.: I have not, but the table of contents looks promising. I'll see if I can find a copy somewhere to take a look at. I like to have a good textbook on my shelf for most subjects I work with, so if I like it this could be a great recommendation, thank you. You could certainly post this as an answer so I can upvote it. – Colin K Apr 20 '11 at 5:04
I should clarify for others who might post answers, I am interested in both textbooks and shorter, online references. For example, I'm a big fan of this sort of thing: Conjugate Gradient Without The Agonizing Pain – Colin K Apr 20 '11 at 5:07
@J.M.: Again, thank you:) These would all be ideal answers if you would like to enter them as answers instead of comments. – Colin K Apr 20 '11 at 5:13
@endolith:Oh, that is an interesting fact indeed. One of the frustrations I've encountered in learning about wavelets is that it is often described as significant, powerful, and novel, but over and over again I hear about the same mundane applications such as compression. I'll be just about to give up hope that there is a new technique for me to learn, when suddenly I'll see some de-noising or feature detection or something that is so accurate it borders on magic, and the author will claim it was done with wavelets. I want to learn that, not read another description of jpeg2000 compression. – Colin K Apr 20 '11 at 21:11

Wavelets and Subband coding, available free now.

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This looks excellent. Perfectly in line with my background as well. – Colin K Nov 6 '11 at 15:16
This book is very good, thanks! – psihodelia Nov 8 '12 at 15:11

If you read French, I would suggest the book Séries de Fourier et ondelettes, Jean-Pierre Kahane, Pierre Gilles Lemarié-Rieusset. ISBN 2-84225-001. See this.

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I am partial to A Wavelet Tour of Signal Processing; The Sparse Way (currently at 3E) by Stéphane Mallat.

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