Time-Frequency Seminar

March 23, 2006

**Special seminar:***Spring Break, Thursday*

**Speaker:**

Roman Vershynin

Department of Mathematics

University of California-Davis

http://www.math.ucdavis.edu/~vershynin/

**Title:**

Robust Quantization and Uncertainty Principles

Abstract:

The uncertainty principle in Harmonic Analysis has been interpreted and enriched in a way to yield algorithms for signal reconstruction (sparse recovery problem). We will see that uncertainty principles can also be used in a natural way to construct robust vector quantizers. Such a quantizer takes a unit vector in Euclidean space and makes its components integers of constant magnitude. Even when an epsilon percentage of coefficients is quantized incorrectly, the quantization error will be of order of epsilon. This is an algorithmic version of Kashin's theorem in asymptotic convex geometry. Open problems will be discussed. [Joint work with Yura Lyubarskii]