### Jeffrey Blanchard (Grinnell College, USA)

#### Greedy algorithms in compressed sensing

*Joint work with Coralia Cartis, Jared Tanner and Andrew Thompson.*

*Wednesday 10 November 2010 at 15.30, JCMB 6206*

##### Abstract

We begin with a review of compressed sensing and the formulation of the
associated combinatorial L0-optimization problem. Using ideas developed for
the convex relaxation (L1-minimization), we'll introduce the phase transition
framework for comparability of sufficient conditions for guarantees on
suboptimal algorithms used to solve the compressed sensing problem. The greedy
algorithms in compressed sensing have guarantees based on the restricted
isometry property and bounding the restricted isometry constants allows for a
translation of sufficient conditions into the phase transition framework.
These theoretical, worst-case guarantees are known to be excessively
pessimistic, hence an average case analysis is desired. We will conclude the
talk with a discussion of our recent GPU implementation of selected greedy
algorithms for the purpose of studying the average case performance.

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