This entry is from Winter semester 2016/17 and might be obsolete. No current equivalent could be found.

# Compressive Sensing (dt. Compressive Sensing)

 Level, degree of commitment Specialization 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(s): Written examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises. Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics. Duration,frequency One semester, Ca. alle 2 Jahre Person in charge of the module's outline Prof. Dr. Götz Pfander

## 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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in Lineare Algebra 1 und 2 sowie Grundlagen der Wahrscheinlichkeitstheorie vermittelt werden.

## Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

• B.Sc. Mathematics
• M.Sc. Data Science
• M.Sc. Mathematics

When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Angewandten Mathematics zugeordnet ist.