Information-theoretic limits of compressed sensing

Abstract: The mathematical roots of compressed sensing can be traced back to the classical Donoho-Stark and Elad-Bruckstein uncertainty relations. In this talk, we develop an information-theoretic framework for compressed sensing, which builds on new probabilistic uncertainty relations inspired by embedding results from dynamical systems theory. Specifically, we consider the problem of recovering analog signals, modeled as general random vectors, from noiseless linear measurements.

This talk represents joint work with D. Stotz, E. Riegler, E. Agustsson, G. Koliander, C. De Lellis, and G. Alberti.