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Wavelets (Winter Semester 2008/09)

Schedule
Lecture: Wednesday 8:00-9:30 Seminarraum 33
Friday 8:00-9:30 Seminarraum 31
Problem class: Friday 11:30-13:00 HS 102
Lecturers
Lecturer Prof. Dr. Andreas Rieder
Office hours: monday, 14:00-15:00, and on appointment
Room 3.040 Kollegiengebäude Mathematik (20.30)
Email: andreas.rieder(at)kit.edu
Problem classes
Office hours:
Room IWRMM (20.52)
Email:

Contents

Wavelet analysis is a rather new, but meanwhile well established, technique for signal and image processing with various applications in other fields. For instance, the famous
JPEG2000 standard for image compression is based upon wavelets.

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In this course we will learn the mathematical foundations of wavelet analysis which belong to the field of harmonic analysis. We will motivate wavelet analysis from the shortcomings
of Fourier analysis with respect to time frequency representations of signals. Then we will study in detail the properties of the integral wavelet transform. The request for efficient evaluation of the wavelet transform leads to the concept of wavelet bases. Here, we will present the construction of orthogonal and bi-orthogonal wavelet systems. Finally, some applications will be discussed: de-noising, image compression, etc.

Literature

  • Louis, Maass, Rieder: Wavelets - Theory and Applications, Wiley 1997
  • Daubechies: Ten Lectures on Wavelets, SIAM 1993
  • Mallat: A Wavelet Tour of Signal Processing, Academic Press 1998
  • Stark: Wavelets and Signal Processing, Springer 2005