A. Bastys
"Wavelet Application in Signal Processing"

Catalog description:

Though wavelet analysis is young, it is used more and more extensively in signal processing, numerical analysis, applied and theoretical physics. Effective representation of signals, data energy concentration and spreading, digital signal denoisening, sound and image features extraction, image rescaling are the most popular areas of wavelet applications. Wavelet analysis gives an understanding of closure connection between continuous and discrete mathematics. An emphasis to the wavelet design techniques will be made. Students may come to the coarse with their own problem at hand requiring some application of wavelets.

Current texts:

Stephane Mallat, A Wavelet Tour of Signal Processing, Academic Press, New York, 1998

Goals:

The goal is to teach students to implement continuos, semi-continuos and discrete wavelet transforms for signal analysis. Students should become familiar with main ideas of sounds and image multiscale analysis. The techniques of wavelet rational scaling, adaptive wavelet filtration, data dimensionality reduction, wavelet based signals time/scale representations will be studied. Students should learn the wavelet denoisening and data compression techniques, and to design orthogonal and biorthogonal wavelets.

Content:

• Mallat's multiresolution analysis
• cascade and direct algorithms for estimation of wavelets
• compactly supported orthogonal wavelets
• fast wavelet decomposition and reconstruction algorithms
• wavelet packets
• wavelet based signal denoisening
• fractional scaling of images
• biorthogonal wavelets
• parametrization of wavelets

Typical requirements:

basic courses in mathematics, algebra and programming are necessary

Helpful background:

experience in using MATLAB