**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.

· Beyond wavelets.

**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**

· Denoising and restoration.

· Image compression.

· Feature extraction.

**Lecture 6: Advanced applications**

· Block-denoising.

· Recovering the derivative from a noisy signal.

· Computing products of functions and matrices.

· Divergence-free wavelets.