Harmonic Analysis: Theory and Applications in Advanced Signal Processing

Dr. Erwin Riegler, Prof. Dr. Helmut Bölcskei

Offered in:
Lecture:Thursday 10:15-12:00, HG F 26.5
The first lecture takes place on Thursday, February 23, 2017, 08:15-10:00.
Discussion session:Thursday 08:15-10:00, HG F 26.5
The first discussion session takes place on Thursday, February 23, 2017, 10:15-12:00.
Instructor:Dr. Erwin Riegler, Prof. Dr. Helmut Bölcskei
Teaching assistant: Dmytro Perekrestenko
Office Hours: Thursday, 15:00-16:00, ETF E 119 (Dmytro Perekrestenko)
Lecture Notes:Lecture notes and problem sets with documented solutions are available.
Credits: 6 ECTS credits

Note: This class will be taught in English. To get credits, you need to pass an oral exam, which will be in German (unless you wish to take it in English, of course). The exam is also required for doctoral students to get credits for the course.


News

We will post important announcements, links, and other information here in the course of the semester, so please check back often!



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, imaging, signal recovery, and inpainting. We will consider theoretical, applied, and algorithmic aspects.

The outline of the course is as follows.

Frame theory:
Frames in finite-dimensional spaces, frames for Hilbert spaces, sampling theorems as frame expansions
Spectrum-blind sampling:
Sampling of multi-band signals with known support set, density results by Beurling and Landau, unknown support sets, multi-coset sampling, the modulated wideband converter, reconstruction algorithms
Sparse signals and compressed sensing:
Uncertainty principles, recovery of sparse signals with unknown support set, recovery of sparsely corrupted signals, orthogonal matching pursuit, basis pursuit, the multiple measurement vector problem
High-dimensional data and dimension reduction:
Random projections, the Johnson-Lindenstrauss Lemma, the Restricted Isometry Property, concentration inequalities, covering numbers, Kashin widths
Prerequisites

The course is heavy on linear algebra, operator theory, and functional analysis. A solid background in these areas is beneficial. We will, however, try to bring everybody on the same page in terms of the mathematical background required, mostly through reviews of the mathematical basics in the discussion sessions. Moreover, the lecture notes contain detailed material on the advanced mathematical concepts used in the course. If you are unsure about the prerequisites, please contact Dmytro Perekrestenko or Erwin Riegler.


Homework Assignments

There will be 6 homework assignments. Every other week a new assignment will be handed out. You can hand in your solutions and get feedback from us, but it is not mandatory to turn in solutions. Complete solutions to the homework assignments will be posted on the course web page.

Homework Problem Sets

Problems Solutions
Homework 1 Solutions to Homework 1
Homework 2 Solutions to Homework 2 Matlab file
Homework 3 Solutions to Homework 3
Homework 4 Solutions to Homework 4
Homework 5 Solutions to Homework 5 Matlab files
Homework 6 Solutions to Homework 6
Lecture Notes

We will use the following book chapter as material for the first few lectures and will send you, by e-mail, the material for the remaining lectures as we go along.

Handouts



Exam

There is an oral exam (in German, unless you wish to take it in English, of course).


Recommended Reading
If you want to go into more depth or if you need additional background material, please check out these books: