Wavelets and Sparsity
Lecturers:
Dr. Simon
Setzer and
Laurent
Hoeltgen
Office hours: TBA
Summer Term 2012
Lectures (3h) with exercises (1h) (6 credit
points)
Time and Location: Tuesday 1214 c.t. and Thursday 1416 c.t.,
Building E1.3, Lecture Hall 001
First lecture: Tuesday, April 17, 2012
Exercises: Every second Thursday instead of a lecture, Laurent
Hoeltgen will present the solution to the exercises.
Announcements –
Description –
Prerequisites –
Lecture Notes –
Assignments –
Exams –
Registration
Literature
Don't forget to schedule an appointment for your oral exam.
The wavelet transform allows us to represent data in a more suitable
"basis". The resulting wavelet coefficients yield interesting ways to analyze
and manipulate the data, e.g., compression (JPEG2000), multiscale analysis of
seismic data, image denoising and inpainting. A central theme is that the
given data is efficiently encoded in only relatively few wavelet coefficents
("sparsity"). We discuss not only the basic theory of the continuous and
discrete wavelet transform but also algorithms and applications in image
processing.
Undergraduate knowledge in mathematics (e.g. ''Mathematik für
Informatiker IIII''). The lectures will be given in English.
Date  Topic  Homework 
17.04. 
Introduction


19.04. 
Mathematical preliminaries

Homework 1 
03.05. 
Fourier Kingdom 
Homework 2, cameraman.pgm, fourier_approximation.c, fourier_approximation_soln.c, plot of the solution (zoomed in) 
15.05. 

Homework 3 
24.05. 
Windowed Fourier Transform 

31.05. 
The wavelet transform 

05.06. 
Parseval's formula for the wavelet transform 
Homework 4 
26.06. 
The wavelet transform (cont.) 
Homework 5,FWT_1d.c, IFWT_1d.c,signal256.txt, FWT_1d_solution.c, IFWT_1d_solution.c 
10.07. 
Redundant representations (Introduction and frames) 

10.07. 
Redundant representations (Ridgelets and curvelets) 
Homework 6, WS12/Homework6_2D_FWT.zip 
26.07. 
Redundant representations (Analysis and synthesis approaches) 

26.07. 
Redundant representations (Optimization theory for the synthesis approach) 

Homework will be assigned biweekly. To qualify for the exam you need 50% of
the points from these assignments.
There will be an oral or a written exam depending on the number of students.
The Registration for the lecture is currently open. Please register
here.
Remember that you also have to register for the exam in
the HISPOS system of the
Saarland University
No textbook is required for this course. Examples of books giving background
material and further reading are:
 Sparse Image and Signal Processing: Wavelets, Curvelets,
Morphological Diversity
J.L. Starck, F. Murtagh and
J. M. Fadili, Cambridge University Press, 2010
 A wavelet tour of signal processing: the sparse way (second
edition)
S. G. Mallat, Academic Press, 2009
 Sparse and Redundant Representations
M. Elad, Springer,
2010
 Ten lectures on wavelets
I. Daubechies, SIAM, 2006
 Wavelets Theory and Application
A. K. Louis, P. Maaß
and A. Rieder, J. Wiley & Sons, Inc., 1997
 Fourier Analysis and Applications
C. Gasquet and P. Witomski,
Springer, 1998
