By and large I try not to flee into cold, formal mathematics, not here. You can find all too many books that will give you just the mathematics (and some of them are invaluable references). On the other hand, sometimes I am way too vague. Let me try to give you a clear statement of what I’m going on about when I say “multiresolution analysis” (MRA).
(Don’t misunderstand me. When I’m studying something, I’m sitting there with collections of definitions, theorems, proofs, and examples – trying to make sense of them. I just think that the collection itself is not a substitute for understanding.)
There’s a lot to be said for having a clearly stated theorem. Working through this has had a large impact on my own grasp of the properties of wavelets.
The most lively summary of multiresolution analysis can be found in the first couple of pages of chapter 5 of Daubechies’ “Ten Lectures on Wavelets”. The most lively introduction can be found on pages 10-16.
I have more than a few, close to several, books that seem to present the following concepts in the same way. First, they use multi-resolution analysis to describe orthonormal wavelets; then they use filter banks to describe biorthogonal wavelets; finally, they explain how biorthogonal wavelets could be described by a modified multi-resolution analysis.
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