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Spring-Summer School Paris IHP 2011

Spring-Summer school [June 20-21-22] in Paris (IHP) with the following two 9 hours courses :

  • Jared Tanner (U. Edinburgh, UK) Stochastic Geometry and Random Matrix Theory in Compressed Sensing. Stochastic geometry and random matrix theory can be used to model and analyse the efficacy of a new paradigm in signal processing, compressed sensing. This new perspective shows that if a signal is sufficiently simple, it can be acquired at a rate proportional to its information content rather than the worst case rate dictated by a larger ambient space containing it. These lectures will show how this phenomenon can be modelled using stochastic geometry, and will also show how standard eigen-analysis in random matrix theory can give similar results.
  • Roman Vershynin (U. Michigan, USA) Introduction to the non-asymptotic analysis of random matrices. This is a mini-course on basic non-asymptotic methods and concepts in random matrix theory. We will develop several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of these methods sprung off from the development of geometric functional analysis in the 1970-2000’s. They have applications in several fields, most notably in theoretical computer science, statistics and signal processing. Two applications will be discussed: for the problem of estimating covariance matrices in statistics, and for validating probabilistic constructions of measurement matrices in compressed sensing.

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