virtuell

Compressive Sensing is a recent development in mathematical signal processing which predicts that vectors that are approximately sparse can be accurately reconstructed from a number of linear measurements that is much smaller than previously believed possible. Efficient algorithms such as convex optimization approaches can be used for the reconstruction. Somewhat surprisingly random matrices model provably optimal measurement schemes. While the most accurate analysis of this phenomenon is available for Gaussian random matrices, practical applications demand for more structure in the measurement matrix. Structured random matrices of particular interest arise from randomly sampling the Fourier transform of the signal as well as subsampling the convolution of the signal with a random vector. We will discuss tools for analyzing the latter type of structured random matrices. It turns out that this leads to bounding the supremum of certain second order chaos processes. In particular, we will present a recent result that provides generic chaining type bounds via gamma-2-functionals. Joint work with Felix Krahmer and Shahar Mendelson.

Hörer sollten sich bitte im Moodle-Raum https://moodle.tu-dortmund.de/enrol/index.php?id=23191 des Seminars anmelden. An alle Angemeldeten werden die Zugangsdaten zum meeting geschickt Weitere Vorträge in der Reihe sind unter http://www.mathematik.tu-dortmund.de/lsix/lehre/WiSe2021/GRK-Seminar/index.php einsehbar.

Holger Rauhut

RWTH Aachen