Wavelets and Sparsity
Lecturer:
Dr. Simon Setzer,
Office hours: Wednesday, 14:1515:15
Summer Term 2011
Lectures (3h) with exercises (1h)
(6 credit points)
Time and Location: Tuesday 1214 c.t. and Friday 1416 c.t., Building E1.3, Lecture Hall 001
First lecture: Tuesday, April 12, 2011
Announcements –
Description –
Prerequisites –
Lecture Notes –
Assignments –
Exams –
Literature
The last set of slides is now online.
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

12.04. 
Introduction 

15.04. 
Mathematical preliminaries 

19.04. 
Mathematical preliminaries (cont.) 
includes Homework 1, due April 26 in class 
26.04. 
Fourier kingdom 

29.04. 
Uncertainty principles 
includes Homework 2, due May 10 in class fourier_approximation.c, cameraman.pgm 
10.05. 
The windowed Fourier transform 

17.05. 
The continuous wavelet transform 
includes Homework 3, due May 27 in class 
27.05. 
The discrete wavelet transform 
includes Homework 4, due June 14 in class FWT_1d.c, IFWT_1d.c,signal256.txt,FWT_1d_solution.c,IFWT_1d_solution.c 
07.06. 
The discrete wavelet transform (cont.) 
Includes Homework 5, due June 24 in class 
11.06. 
Redundant representations 

21.06. 
Ridgelets and curvelets 

01.07. 
Analysis and synthesis approaches 
includes Homework 6, due July 8 in class 
05.07. 
Optimization theory for the synthesis approach 

15.07. 
Optimization theory for the synthesis approach (cont.) 

Homework will be assigned biweekly. To qualify for the exam you need 50% of the points from these assignments.
Please register for the lecture: 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
