- Week 1:
- Introduction and Overview.
- Why wavelets, subband coding and multiresolution signal processing.
- The course at coarse resolution.
- Week 2:
- Fourier theory, sampling, signal processing, time-frequency
- Hilbert spaces, orthonormal bases.
- Week 3:
- Multirate signal processing: review
- Discrete-time bases.
- Week 4:
- Analysis of Haar and Sinc Expansions of Discrete-Time Signals.
- Orthonormal and Linear Phase filter banks.
- Week 5:
- Construction of Daubechies filters.
- Lattice Factorization of Filter Banks.
- Week 6:
- Construction by lifting: "next-generation" wavelets.
- Tree-structured filter banks and Wavelet-Packets.
- Week 7:
- Multichannel Filter Banks / IIR filter banks.
- Discrete-Time Wavelet Series.
- Week 8:
- Lapped Orthogonal Transforms.
- Series Expansions of Continuous-Time Signals.
- Haar and Sinc wavelets.
- Week 9:
- Multiresolution concept and analysis.
- Wavelets derived from iterated filter banks: Regularity.
- Week 10:
- Wavelet Series: Mallat's algorithm.
- Continuous Wavelet Transform and Frames.
- Week 11:
- Adapted wavelet and wavelet packet representations.
- Best Bases algorithms.
- Arbitrary tilings of the time-frequency plane based on wavelets.
- Week 12:
- Applications to signal compression.
- Review of Rate-Distortion, KLT, Optimal Bit Allocation principles.
- Basics of Quantization Theory.
- Week 13:
- Applications to image and video compression.
- State-of-the-art wavelet image coders:
- Role of wavelets in next-generation image compression
- Week 14:
- Applications of multiresolution concept to communications/networking:
- Joint source-channel coding, broadcast and multicast.
- Video over the Internet and Wireless Channels.
- Week 15:
- Other applications: Denoising & restoration, telecommunications,
- computer graphics, etc. (time-permitting).
Last modified:August 10 1999