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Wavelets (Winter Semester 2013/14)

Lecture: Tuesday 9:45-11:15 1C-04
Wednesday 11:30-13:00 1C-03
Problem class: Thursday 15:45-17:15 Z 2
Lecturer Prof. Dr. Andreas Rieder
Office hours: Until further notice only on appointment.
Room 3.040 Kollegiengebäude Mathematik (20.30)
Email: andreas.rieder(at)kit.edu
Problem classes Dr. Tim Kreutzmann
Office hours:
Room Kollegiengebäude Mathematik (20.30)


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.
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, if time permits, some applications will be discussed: de-noising, image compression, etc.

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