How to learn the wavelet transform? Is there any good literature if I want to learn the wavelet transform? Especially my project is related with marine electromagnetism?
 A: The two most commonly referenced textbooks on wavelets with which I am familiar are Ingrid Daubechies's Ten Lectures on Wavelets and Strang and Nguyen's Wavelets and Filter Banks. Both books do a good job of laying out the basic mathematics of wavelets; Strang and Nguyen's book is more applications-driven, while Daubechies's presentation is more theoretical in scope and style.
Of course, the best way to learn how to use wavelets is to actually "play with them" in a hands-on environment such as Matlab or iPython.
A: Kaiser has A Friendly Guide to Wavelets. The introduction is nice but it introduces the continuous wavelet transform (CWT) by way of the windowed Fourier transform which is not necessary; there is a nice connection between the two as Daubechies covers as well, but I found this approach confusing.
Daubechies is obviously great (she was one of the founders of the theory) but requires a fair bit of mathematical maturity. Conversely, you can easily find 100+ engineering/applied books on wavelets - the intuition here is nice; however, as you may find with wavelets, to gain something, you lose something else - in particular, a lack of understanding on the choice of mother wavelet, the admissibility constant, and it's highly doubtful they will mention any topological vector spaces where the wavelets live. This is a considerable sacrifice as choosing the correct wavelet for your situation may be very important. Of the more applied books I've looked through, The Illustrated Wavelet Transform Handbook has been my favorite.
A: Right now, I'm using a book entitled " An Introduction to Wavelets through Linear Algebra" by Micheal Frazier. Published in 1999, it's still a pretty good book, and contains a nifty refresher to linear algebra as well.
