Lectures: MWF 10-11 am, 2 Evans

Prof: J Strain, email strain@math.berkeley.edu , WWW http://math.berkeley.edu/~strain/

Office Hours: Wed 2:10-3 and 5:10-6, Thu 3:10-4 or by appointment, in 1099 Evans.

Final Week Office Hours: Mon 9:30-11,Thu 10-12, Sat 11-12.

Course Web page: http://math.berkeley.edu/~strain/118.S03/

Course Control Number: 54945

Prerequisites: Math 53 and 54 or equivalent.

Required Text: S. Mallat A Wavelet Tour of Signal Processing, 2nd edition, Academic Press, 1999.

Syllabus: The course will cover the basic mathematical theory and practical applications of wavelets and related ideas to signal and image processing:

• Fourier analysis (Chapter II). Linear time-invariant filtering, properties of Fourier integrals and transforms, the uncertainty principle and total variation analysis. Two-dimensional Fourier analysis.
• Discrete signal processing (Chapter III). Sampling and aliasing, discrete filters, Fourier series, fast Fourier transforms, and discrete image processing.
• Time-frequency tradeoffs (Chapter IV). Atoms, windowing, basic wavelet transforms.
• Wavelet zoom (Chapter VI). Lipschitz regularity, vanishing moments, edge detection.
• Wavelet bases (Chapter VII). Orthogonal bases, filter banks, and separable bases.
• Approximation with wavelets (Chapter IX). Linear and nonlinear techniques. Image approximation and adaptive basis selection.
• Transform coding (Chapter XI). Signal compression, quantization, high bit rate compression, image and video compression.

Grading: Grades will be based on the best 7 problem sets (60%) and final project (40%). Problem sets will be due every Friday in class, and late submissions will not be accepted after solutions are distributed. Final project presentations will be made during the last week, and the written report on the final project will be due at the final exam time, 11 am Monday 5/19/03. (Please bring it to my office, 1099 Evans, or e-mail it, rather than to the final exam room.)

Reading and homework assignments (revised 4/18/03)

Supplementary exercises (in PDF format)

Problem Solutions