Prerequisites for understanding Wavelet theory

Question

I have a degree in computer science and I have taken the following math courses.

• Calculus I
• Calculus II
• Discrete Mathematics and Number Theory
• Linear Algebra
• Probability
• Logic
• Automata Theory

What other courses should I take in order to prepare for studying wavelets, with a focus of implementing wavelet transforms?

EDIT:

Looks like this was closed for not being "programming related". That is wrong!

Wavelet transform is a very common image processing technique, it's used in H.264 and JPEG2000. Is image processing beyond the scope of StackOverflow?

Inhere

Interesting meta-question. Does programming in mathematical sense count? From what I recall Jeff Attwood saying, SO is about programming with a computer. But you can do this kind of programming mathematically.... – Gotham

If you know your linear algebra well, that's really all you need to know. However, very few people really know linear algebra after one course. – Austen

Why is this closed? It's very programming related. – Inhere

if it doesn't get reopened, try here gamedev.net/community/forums/forum.asp?forum_id=20 – Acciaccatura

Of course this is programming related. Does anyone in this forum ever actually study for their profession? Its freakin' embarrassing. – Carty

For the record, you should probably know and understand Fourier Transforms, since Wavelet Transforms are a concept derived from them. – Carty

Answer 1

On top of what you've got there already, I would recommend signal processing or some similar course that covers Fourier transforms and the like. Besides being useful as a foundation for wavelets, Fourier theory will give you a new way of looking at data that is often useful. Wavelets will probably be part of the curriculum for more advanced signal processing courses.

Shocking

+1 for Signal Processing. Understanding aliasing and other SP concepts help! – Normally

Answer 2

Linear algebra and calculus may help you there, but not much else. You'll also want to look at complex analysis and differential equations.

Orvas

False. If you want to understand the math behind wavelet compression, and most importantly quantify the compression error, you'll have to understand difficult exotic functional analysis topics like Besov spaces and weak-L^p. – Duckweed

Old comment, but which part of my answer was false? I stated that, of the topics he listed, linear algebra and calculus were the useful ones. – Orvas

Answer 3

It sounds to me like you should just start learning about wavelet transforms and then figure out gaps along the way. They're not that involved. Fourier transforms etc are just an example of an orthogonal basis that is part of linear algebra.

Gecko

Answer 4

Depends whether you want to learn about discrete or continuous wavelet transforms. If discrete then you'll need basic Fourier theory, linear algebra and complex number theory. If continuous then you'll need advanced Fourier theory and stationary phase approximations.

If you want to do research then I'd recommend learning both discrete and continuous. Most people only know one or the other in detail and it is seriously stifling research. There is a lot of opportunity for cross pollination here.

Disapproval