DR. MARTIN MOHLENKAMP
Ohio University
Athens, Ohio
mjm@math.ohiou.edu

Wavelets and Partial Differential Equations

Lecture 1: Time/Frequency Analysis
· Fourier analysis.
· Windowed Fourier transform.
· Wavelet transform.

Lecture 2: Fast Algorithms and Applications
· Multiresolution Analysis.
· Filter banks.
· Lifting schemes.
· Signal/Image compression, denoising.

Lecture 3: Main Characters
· Pre-wavelets: splines, orthogonal polynomials, etc.
· Wavelets: Haar, Meyer, Daubechies, Coiflets, symmlets, etc.
· Post-wavelets: brushlets, edgelets, ridgelets, etclets.

Lecture 4: Variations over a Theme
· Wavelet packets and local cosine bases.
· Biorthogonal wavelets.
· Wavelets on the interval.
· Multiwavelets.

Lecture 5: Applications to Signal/Image Processing
· Representation of d/dx in wavelet bases.
· Pointwise products.
· Interpolation of sample values.
· Characterization of Sobolev spaces.