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Wavelets (Wintersemester 2013/14)

Vorlesung: Dienstag 9:45-11:15 1C-04
Mittwoch 11:30-13:00 1C-03
Übung: Donnerstag 15:45-17:15 Z 2
Dozent Prof. Dr. Andreas Rieder
Sprechstunde: Montag, 14:00-15:00Uhr, und nach Vereinbarung
Zimmer 3.040 Kollegiengebäude Mathematik (20.30)
Email: andreas.rieder(at)kit.edu
Übungsleiter Dr. Tim Kreutzmann
Zimmer 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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