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Harmonic Analysis: Theory and Applications in Advanced Signal Processing
Prof. Dr. H. Bölcskei
Offered in:
- Doctoral and Post-Doctoral Studies: Department of Information Technology and Electrical Engineering
- Electrical Engineering and Information Technology Master: Recommended Subjects (Empfohlene Fächer)
- Mathematics Master: Selection: Further Areas (Auswahl: Weitere Gebiete)
- Physics Master: General Electives (Allgemeine Wahlfächer)
- Computational Science and Engineering Master: Electives (Wahlfächer)
| Lecture: | Wednesday 13:15-15:00, ETZ E6, starting February 23, 2011
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| Discussion session: | Wednesday 15:15-17:00, ETZ E6, starting February 23,
2011 |
| Instructor: | Prof. Dr. Helmut Bölcskei |
| Teaching Assistant: | Veniamin Morgenshtern |
| Office Hours: | Wednesday, 17:00-18:00, ETF E 118 |
| Lecture Notes: | Lecture notes and problem sets with documented solutions are available. This year, we will teach new subjects with corresponding lecture notes being made available as we go along during the semester. Please have a look at the section on recommended reading for further details. |
| Credits: | 6 ECTS credits |
Note: This class will be taught in English. The oral exam will be in German (unless you wish to take it in English, of course).
To get credit for this class, you need to complete four out of six homework assignments and pass an oral exam. The exam is also required for doctoral students.
News
We will post important announcements, links and other information here during the course of the semester, so please check back often!
- Apr. 22, 2011: We have finalized the book chapter on Frame Theory. You can download the updated version here
- Feb. 23, 2011: Lecture notes are online
- Dec. 18, 2010: Web page is updated
Course Info
This course is an introduction to the field of applied harmonic analysis with emphasis on applications in signal processing such as transform coding, inverse problems, and imaging. We will consider theoretical, applied, and algorithmic aspects.
The outline of the course is as follows.
Frame theory and sampling: Hilbert space basics, frames for Hilbert spaces, sampling theorems
Wavelets and Gabor expansions: Continuous and discrete wavelet transforms, multiresolution analysis, Gabor expansions, Weyl-Heisenberg
frames, density theorems
Sparse signals and compressed sensing:
Uncertainty principles, signal recovery from partial information, sparse signals, random measurements, orthogonal matching pursuits,
reconstruction via linear programming
High-dimensional data and dimension reduction:
Random projections, kernel principal component analysis, the Johnson-Lindenstrauss lemma
Matrix completion
Prerequisites
The course is heavy on linear algebra, operator theory, and functional analysis. A solid
background in these areas will be beneficial, albeit we will spend the first discussion sessions
trying to bring everybody on the same page in terms of the mathematical background required. The lecture notes already available discuss all advanced mathematical concepts used in the course from scratch. If you are unsure about the prerequisites, please contact H. Bölcskei or V. Morgenshtern.
Homework Assignments
There will be 6 homework assignments. The Testat will be given to students who have handed in 4 acceptable solutions (3 in case you are serving in the army during the semester). Every 2nd week, a new assignment will be handed out, and you should submit the solutions two weeks later. The day an assignment is due, a complete solution will be posted.
You are allowed to resubmit one rejected submission until the end of the
semester.
The assignments are due on the date indicated, either in class or in the discussion session. We do not accept late homeworks because the solutions will be posted on the website.
Homework Problem Sets
You can order the lecture notes by clicking the links below.
Most of the handouts from class will be posted here, except for the ones where copyright issues prevent us from doing so.
Exam
There is an oral exam (in German, unless you wish to take it in English).
If you want to go into more depth or if you need additional background, please check out these books and papers:
- S. Mallat, ''A wavelet tour of signal processing: The sparse way'', 3rd ed., Elsevier, 2009
- I. Daubechies, ''Ten lectures on wavelets'', SIAM, 1992
- O. Christensen, ''An introduction to frames and Riesz bases'', Birkhäuser, 2003
- K. Gröchenig, ''Foundations of time-frequency analysis'', Springer, 2001
- M. A. Pinsky, ''Introduction to Fourier analysis and wavelets'', Brooks/Cole Series in Advanced Mathematics, 2002
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