Computer Science, applied math majors and math majors with emphasis in Comp. Sci. Graduate students in related areas.
The goal of this course is to provide graduate students and advanced undergraduate students with an introduction to the mathematics and practice of Data Representation. The focus of this course will be on wavelet decompositions and spline representation, partly because of the prominence of these topics in Data Representation, and partly because these are the specialty topics of the instructor.
- Introduction to Fourier series and Fourier transform
- Time-frequency localization
- Wavelets and frames (analysis and synthesis, orthogonal wavelets, biorthogonal wavelets, tight frames)
- Applications: denoising and compression of signals and images
- Interpolation and approximation by splines (interpolation, least-squares approximation, smoothing, quasi-interpolation and other local methods)
- Splines as linear combinations of B-splines
- Knot insertion and subdivision
- Free-knot spline approximation
- Splines in CAGD