M/611

In compressed sensing and high-dimensional statistics, one is faced with the problem of reconstructing a high-dimensional vector x from underdetermined, possibly noisy linear measurements y=Ax. Research from the last decade has shown that this can be done in a computationally efficient way if one knows that the target vector x is sparse or, more generally, comes from a ``low-complexity`` model. The best known reconstruction results are known for ?well-behaved? random measurement matrices, e.g., Gaussian matrices. In this talk I will consider the problem of recovering x via a convex program, called \ell_p-constrained basis pursuit, in the scenario that A contains heavy-tailed random variables. I will present recent work that shows that under surprisingly light conditions on the distribution on the entries, one can reconstruct x from an optimal number of measurements. If time permits, I will show an application to reconstruction from quantized heavy-tailed measurements. I will not assume any prior knowledge of compressed sensing during the presentation. Based on joint work with Guillaume Lecué (Ecole Polytechnique) and Holger Rauhut (RWTH Aachen University).

Vortrag am Donnerstag dem 27. April 2017 um 16.15 im Seminarraum M/611.

Sjoerd Dirksen

RWTH Aachen