Explicit Euclidean Sections, Codes over the Reals and Expanders
Seminar Room 1, Newton Institute
AbstractHere is a basic problem, which comes under various names including "compressed sensing matrices", Euclidean sections of L1", "restricted isometries" and more. Find a subspace X or R^N such that every vector x in X has the same L1 and L2 norms (with proper normalization) up to constant factors. It is known that such subspaces of dimension N/2 exist (indeed "most" of them are), and the problem is to describe one explicitly. I will describe some progress towards this problem, based on extending the notion of expander codes from finite fields to the reals.
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