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Course Description: Compressed Sensing (0432 L 664)

Course Objectives

The estimation of signals and system parameters is an important issue in several communication and information processing tasks. Conventionally, linear estimation in the least-square sense is often used when the data to be estimated is not a-priori compressible. The number necessary observations scales then linearly with the number of unknown parameters. However, considerable less measurements are necessary if additional low-complexity structure is taken into account. At the core of compressive sensing (CS) lies the discovery that it is possible to reconstruct a sparse signal exactly from an underdetermined linear system of equations and that this can be done in a computationally efficient manner via convex methods. This course will give a theoretical introduction into this new paradigm.
Course Content
  1. Introduction and outline of the course (motivation, single-pixel camera)
  2. Background on conventional linear estimation (least-squares, regularizations, Gauss-Markov estimate, Cramer-Rao etc.)
  3. Sparse Solutions to Underdetermined Lin. Equations (spark)
  4. Coherence, Welsh-bounds, frames and redundancy, union of bases
  5. Nullspace property and best k-term approximation
  6. Noisy sparse estimation
  7. Restricted isometry property (RIP)
  8. Random matrices and the RIP property (stable low-dimensional embeddings)
  9. l1 minimization and algorithms
Mainly intended for Study Programs
  • Elektrotechnik MSc; 1-3
  • Technische Informatik MSc; 1-3
  • Informatik MSc; 1-3
  • Technomathematik MSc; 1-3
  • Wirtschaftsingenieurw. MSc/Elektrotechnik; 1-3
Course Supporting Material:
  1. D.G. Luenberger, "Optimization by vector space methods" 1969, Wiley
  2. M. Elad, "Sparse and Redundant Representations - From Theory to Applications in Signal and Imaging Processing", 2010, Springer
  3. Y.C. Eldar and G. Kutyniok, "Compressed Sensing: Theory and Applications", 2012, Cambridge University Press
  4. S. Foucart and H. Rauhut, "A Mathematical Introduction to Compressive Sensing", 2013, Birkhauser

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COURSE - Compressed Sensing

LV-Nr. 0432 L 664
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Dr.-Ing. Peter Jung
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