Selected Topics in ASC (STASC)5 ECTS
(englische Bezeichnung: Selected Topics in ASC)
(Prüfungsordnungsmodul: Selected Topics in ASC)

Lehrveranstaltungen:

• • Selected Topics in ASC
    (Vorlesung, 4 SWS, Antonia Maria Tulino, Einzeltermine am 2.5.2018, 5.5.2018, 7.5.2018, 9.5.2018, 14.5.2018, 16.5.2018, 23.5.2018, 26.5.2018, 28.5.2018, 30.5.2018, 4.6.2018, 6.6.2018, 11.6.2018, 13.6.2018)
  • Supplements for Selected Topics in ASC
    (Übung, Antonia Maria Tulino, Zeit und Raum n.V.)

Empfohlene Voraussetzungen:

Prerequisite: Familiarity with the following subjects:
• probability theory
• Basic of statistical estimation, model selection, and decision theory
• linear algebra
• basic convex analysis and optimization

Inhalt:

Content:
Course Description: The Shannon/Nyquist sampling theorem asserts that information is not lost when capturing a signal, if the signal is sampled at least two times faster than the signal bandwidth. In many applications, the Nyquist rate is either so high to make compression a necessity prior to storage or transmission or very expensive. Compressed sensing is a new sampling/data acquisition theory stating that sparsity or compressibility can be exploit when acquiring signals of general interest so that nonadaptive sampling techniques, that condense the information of a compressible signal into a small amount of data, can be designed. This fact has profoundly changed signal acquisition in areas ranging from analog-to-digital conversion, digital optics, magnetic resonance imaging, and seismic. Syllabus:
• Sparsity
• L1 minimization
• Probabilistic approach to compressed sensing
• Deterministic approach to compressed sensing
• Robustness versus noise
• Model selection in linear models
• Lasso: algorithms and extensions
• Gaussian graphical models and graphical lasso
• Smooth convex optimization: optimal first-order methods (Nesterov's algorithm), complexity analysis
• Nonsmooth convex optimization: smooth approximations of nonsmooth functions, prox-functions, Nesterov's algorithm
• Mirror-descent algorithms
• Nuclear-norm minimization

Lernziele und Kompetenzen:

The students analyze and explain recent research results presented by prominent guest professors with high international scientific reputation. The students incorporate the addressed topics and research results into their own experiences and knowledge in signal processing and communications. They use the material presented in this course in their major or minor project and/or in their Master Thesis. They develop new scientific results in the addressed research fields.
The main objective of the course is to give students a sense of real applications that might benefit from compressive sensing ideas emphasizing the many connections with information theory, statistics, and probability theory and exposing students to recent ideas in modern convex optimization allowing rapid signal recovery or parameter estimation. Specifically it will cover 1) the basic mathematical theory, showing when it is possible to reconstruct sparse or nearly sparse signals from undersampled data 2) efficient numerical methods in large-scale convex optimization for reconstructing signals from compressive samples 3) progress in implementing compressive sensing ideas into acquisition devices.

Bemerkung:

Recommended: Courses on Information Theory, Statistical Signal Processing, Digital Communications, Source and Channel Coding

Organisatorisches:

Evaluation: There will be a few homework assignments that involve both theory and programming components. A hard copy of your homework is required. Students are encouraged to use LaTeX to typeset their homeworks. A final project, at the end of the course, will be also assigned. The final evaluation will be based on the homework assignments, the project and an oral exam.

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Advanced Signal Processing & Communications Engineering (Master of Science)
   (Po-Vers. 2016w | TechFak | Advanced Signal Processing & Communications Engineering (Master of Science) | Masterprüfung | Pflichtmodule | Selected Topics in ASC)

Studien-/Prüfungsleistungen:

Selected Topics in ASC (Prüfungsnummer: 318031)

(englischer Titel: Selected Topics in ASC)

Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 30, benotet, 5 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

Prüfungssprache: Englisch

Erstablegung: SS 2018, 1. Wdh.: WS 2018/2019

1. Prüfer:

Antonia Maria Tulino