Wavelets have become part of the toolbox of scientist. Wherever a signal or image
needs to be analyzed, the wavelet transform can be used. Wavelets provide a "mathematical
zoom" that permits one to analyze functions and operators at many scales
simultaneously. Wavelets have wonderful approximation properties. From the mathematical
point of view they provide bases for a number of classical spaces of functions.
From the practical point of view they permit to represent certain signals very
efficiently. Wavelets are being used to study turbulence and PDE's. They also
have become a popular denoising tool. In this course, Dr. Pereyra will explain:
(a) the basics of wavelets and signal/image compression; (b) how to construct
divergence-free multi-wavelets which are expected to be useful in numerical analysis
of incompressible fluids; (c) denoising procedures and compare wavelet techniques
to classical denoising techniques; and (d) what wavelets are, how to construct
them, and how to implement them.