Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, October 25, 2018, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Lenny Fukshansky (Claremont McKenna College)

We investigate the problem of constructing m by d matrices A with small entries and d large comparing to m so that for all integer vectors x in R^d with at most m nonzero coordinates the Euclidean norm of the image vector Ax is bounded away from 0 by an absolute constant. A bound like this allows for robust recovery of the original sparse vector x from its image Ax. This problem is motivated by the compressed sensing paradigm and has numerous potential applications ranging from wireless communications to medical imaging. We use a combination of combinatorial, probabilistic and number-theoretic methods to discuss existence and some constructions of such sensing matrices with concrete examples. We also discuss limitations of our constructions, stemming from sparse variations of some classical results in the geometry of numbers. This is joint work with D. Needell and B. Sudakov.

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