Lecture Image and Geometry Processing I:

Applied Fourier Analysis

Winter term 2020/21
Lecture
Tuesdays, 10.15 Uhr - 11.55 Uhr, online
Fridays, 10.15 Uhr - 11.45 Uhr, online
First lecture: November 3, 2020

Exercises
Time and Room will be determined.

Participants:
The lecture is suitable for students in mathematics, physics and computer science.

Assumptions to finish the lecture successfully:
There will be a written examination (120 minutes) in February 2021.

Assumptions to get admission for the examination:
Attendance of the exercises and 50 percent of the achievable points for homework. With this lecture + exercises you can obtain 9 ECTS points.

Content:
This Lecture Image and Geometry Processing I is concerned with topics from Applied Fourier Analysis. In particular we will focus on the following topics:

1. Introduction
2. Fourier series: Properties, convergence, applications in signal processing
3. Fourier transform: Properties, convergence, applications in signal processing
4. Discrete Fourier transform (DFT): finite convolution, fast algorithms, applications
5. Wavelet transform: scaling functions, multiresolution analysis (MRA), construction of wavelet bases, filter banks of perfect reconstruction
6. Applications in signal denoising and compression

In the next term a Lecture Image and Geometry Processing II will be offered that will focus on numercal methods of image compression and image denoising.

Literature:

G. Plonka, D. Potts, G. Stedl, M. Tasche, Numerical Fourier Analysis, Birkhäuser, Basel, 2018.
H. Babovsky, T. Beth, H. Neunzert, M. Schulz-Reese, Mathematische Methoden in der Systemtheorie: Fourieranalysis, B.G. Teubner, Stuttgart, 1987.
G. Steidl und M. Tasche, Schnelle Fouriertransformation - Theorie und Anwendungen, Lehrbriefe der FernUniversität Hagen, 1996.
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, San Diego, 1999.
C. Van Loan, Computational Frameworks for Fast Fourier Transform, SIAM, Philadelphia, 1992.
K.D. Kammeyer, K. Kroschel: Digitale Signalverarbeitung, Teubner, Stuttgart, 1998.
M. Hanke-Bourgeois: Grundlagen der Numerischen Mathematik und des Wissenschaftlichen Rechnens, Teubner, Stuttgart, 2002.
A.K. Louis, P. Maaß, A. Rieder: Wavelets: Theorie und Anwendungen, Teubner, Stuttgart, 1998.