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German original

Compressive Sensing
(dt. Compressive Sensing)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements
6 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
Ca. alle 2 Jahre
Person in charge of the module's outline N.N.

Contents

Compressive Sensing deals with the measurability of sparsely populated signals on the basis of at first glance insufficient information. Well-known applications are the so-called ''one pixel camera'' and computer tomography.

After a detailed discussion of the basics from linear algebra, probability theory, optimization and functional analysis, we systematically work out the fundamental results of the area. Results on null space and restricted isometry property of measurement matrices allows to establish algorithms (Basis Pursuit, Orthogonal Matching Pursuit) which can decode sparse data vectors on the basis of only few measurements.


Qualification Goals

Students gain experience in relation to

  • modelling in applied mathematics,
  • the need to develop fast algorithms,
  • combining methods from different mathematical disciplines,
  • using connections of different applications of a theory.

Prerequisites

None. The competences taught in the following modules are recommended: Linear Algebra I, Linear Algebra II, Probability Theory.


Recommended Reading

  • A Mathematical Introduction to Compressive Sensing, 2013 Springer Verlag, Simon Foucart und Holger Rauhut.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2020/21. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.