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Wavelets and Sparsity

Summer Term 2014

Wavelets and Sparsity

Lecturer: Laurent Hoeltgen,
Office hours: Tuesday, 14:00-16:00
Examiner: Prof. Dr. Joachim Weickert
Lectures (3h) with exercises (1h)
(6 credit points)

Time and Location:
Monday 16-18 in Building E1 3, HS 001
Thursday 14-16 in Building E1 3, SR 016

First lecture: Thursday, April 17th.

Announcements – Description – Prerequisites – Lecture Notes – Assignments – Exams – Registration Literature

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 I-III''). It is assumed, that basic concepts from real analysis and linear algebra are known. The lectures will be given in English.

The slides from the lecture will usually be uploaded here shortly after the lecture. Nevertheless, Students are encouraged to visit the lecture, as supplementary useful results might be given in the lecture that do not figure on the slides. CDF files can be opened with the CDF-Player from Wolfram, which is freely available from here.

Date	Topic	Homework
17.04.2014	Introduction Matlab Code Sound Procesing Example
21.04.2014	Public Holiday, No Lecture (Ostermontag)	---
24.04.2014	Vector Spaces I
28.04.2014	Vector Spaces II	Assignments due 05.05.14
01.05.2014	Public Holiday, No Lecture (Tag der Arbeit)	---
05.05.2014	Tutorial	Missing part of example solution.
08.05.2014	Fourier series and discrete Fourier transform	CDF Player, Fourier Series Demo, Gibbs Phenomen Demo, Aliasing Demo
12.05.2014	Fourier Transform, Uncertainty Principles and Windowed Fourier Transform	Assignments due 19.05.14 Programming Assignment Code
15.05.2014	Continuous Wavelet Transform I	Proof of Parseval's identity
19.05.2014	Tutorial
22.05.2014	Continuous Wavelet Transform II	---
26.05.2014	Multi Resolution Analysis and Fast Wavelet Transform	Example Solution Programming Assignment
29.05.2014	Public Holiday, No Lecture (Christi Himmelfahrt)	---
02.06.2014	Lecture	Assignments due 12.06.14
05.06.2014	Biorthogonal and higher dimensional Wavelets, Redundant Represenations I	Assignments due 23.06.14 Programming Assignment Code
09.06.2014	Public Holiday, No Lecture (Pfingstmontag)	---
12.06.2014	Tutorial
16.06.2014	Redundant Representations II
19.06.2014	Public Holiday, No Lecture (Fronleichnam)	---
23.06.2014	Tutorial	Assignments due 30.06.14 Programming Assignment Code
26.06.2014	Redundant Represenations III	---
30.06.2014	Tutorial	Assignments due 07.07.14
03.07.2014	Redundant Representations IV
07.07.2014	Tutorial
10.07.2014	Redundant Representations V	---
14.07.2014	Redundant Representations VI
17.07.2014	Ridgelets and Curvelets I (This lecture is not relevant for the exam)
21.07.2014	Ridgelets and Curvelets II
24.07.2014	Exam (16:00-18:00, Building E 1.3, HS 001)	---
02.10.2014	Exam (14:00-16:00, Building E 1.3, HS 001)	---

Homework will be assigned bi-weekly. To qualify for the exam you need 50% of the points from these assignments. Submission in groups of at most 2 people is recommended. The admission to the exam is valid for both exams. Everybody who is admitted to the first exam is automatically admitted to the second exam, too.

There will be two exams. The first one will be on July 24th, 2014 from 16:00-18:00 in Building E 1.3, HS 001. The second exam will take place on October 2nd, 2014 from 14:00-16:00 in E1.3 HS 001. These will be closed books exams lasting 2 hours. People admitted to the exams are allowed to participate in both exams. The better grade counts.

In order to register for the Lecture, write an e-mail to Laurent Hoeltgen. The subject line must begin with the tag [WS14]. Further, please provide the following information: first name, last name, date of birth, student ID number (e.g. Matrikel), course of study (e.g. Bachelor, Master, ...), subject of your studies (e.g. computer science, mathematics, ...). These information are necessary to give you credit points for a successful participation in the lecture at the end of the semester. Please ensure that the provided information is correct. Note that the e-mail address from which you send this information will be used to provide you with urgent information concerning the lecture. Therefore, use an address, that you check regularly. Finally, this registration is for internal purposes at our chair only and completely independent of any System like LSF/Hispos. They require a separate registration.

No textbook is required for this course. Examples of books giving background material and further reading are:

1. Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity
   J.-L. Starck, F. Murtagh and J. M. Fadili, Cambridge University Press, 2010
   
   
2. A wavelet tour of signal processing: the sparse way (second edition)
   S. G. Mallat, Academic Press, 2009
   
   
3. Sparse and Redundant Representations
   M. Elad, Springer, 2010
   
   
4. Ten lectures on wavelets
   I. Daubechies, SIAM, 2006
   
   
5. Wavelets Theory and Application
   A. K. Louis, P. Maaß and A. Rieder, J. Wiley & Sons, Inc., 1997
   
   
6. Fourier Analysis and Applications
   C. Gasquet and P. Witomski, Springer, 1998
   
   

These books are also available in the library. See here for the exact locations of the books in the library.

Last change: Laurent Hoeltgen, 16.04.2014

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