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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](http://www.cs.nyu.edu/cs/faculty/mallat/book.html)?2011-04-20
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    @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.2011-04-20
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    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](http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)2011-04-20
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    [Daubechies's lectures](http://www.ec-securehost.com/SIAM/CB61.html) are a bit heavy on the mathematical machinery, but you can look at them if more detail is needed and/or you want to look at underpinnings.2011-04-20
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    @J.M.: Again, thank you:) These would all be ideal answers if you would like to enter them as answers instead of comments.2011-04-20
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    Just wait a bit, J.M. is probably building up a bibliography. ;)2011-04-20
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    I'm in the same boat of familiarity with Fourier but not understanding wavelets. One thing I've discovered that seems to "bridge the gap" is the complex Morlet wavelet, which is just a Gaussian-windowed blip of sinusoid, making the transform behave similarly to the STFT, which breaks things up into windowed blips of sinusoid.2011-04-20
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    @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.2011-04-20
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    @J.M.isn'tamathematician your link is down.2017-05-12
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    @LeGrand, you could've saved me the trouble of figuring out which [link](http://dx.doi.org/10.1137/1.9781611970104) was kaput.2017-05-12

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