Compressed Sensing

Philipp Walk is a member of IEEE and he received his Dipl.-Phys in mathematical physics in 2006 from the Technical University of Berlin (TUB), Berlin, Germany. He has been with the Department of Mobile Communications at TUB since 2007 and the Department of Theoretical Information Technology at the Technical University of Munchen (TUM), Munich, Germany since 2010. He received his Dr.-rer.nat (Ph.D.) degree in 2014 (on Convolutions with Support Restrictions) from TUM and is currently working under the DFG grant WA 3390/1-1 at the California Institute of Technology, Pasadena, CA, United States, in the field of signal processing and communication theory. His current research interests are in the area of compressed sensing, Fourier analysis, time-frequency analysis and additive combinatorics. He has also been giving lectures on compressed sensing at TUM since 2014. Peter Jung is a Member of IEEE and VDE/ITG. He received the Dipl.-Phys. in high energy physics in 2000 from Humboldt University, Berlin, Germany, in cooperation with DESY Hamburg. He has been with the Department of Broadband Mobile Communication Networks at Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut (HHI) since 2001 and the Fraunhofer German-Sino Lab for Mobile Communications since 2004. He received his Dr.-rer.nat (Ph.D.) degree in 2007 (on Weyl--Heisenberg representations in Communication Theory) from the Technical University of Berlin (TUB), Germany and is currently working under DFG grants JU 2795/1-/&2/&3 at TUB in the field of signal processing and information and communication theory. His current research interests are in the area of compressed sensing, time-frequency analysis, dimension reduction and randomized algorithms. He has also been giving lectures in compressed sensing and estimation theory.

Introduction.- Signal Representation.- Least-Squares Estimation in Finite Dimensional Subspaces.- Sparse Solutions to Underdetermined Linear Equations.- Sparse Estimation from Noisy Measurements.- Random Sampling.- Low-Rank Matrix Recovery & Beyond.- Numerical Reconstruction.- Prelim: Compactness and Approximation.