The story of three polytopes and what they tell us about information acquisition

17 November 2008
Dr. Jared Tanner
We will examine the typical structure of random polytopes by projecting the three fundamental regular polytopes: the simplex, cross-polytope, and hypercube. Along the way we will explore the implications of their structure for information acquisition and optimization. Examples of these implications include: that an N-vector with k non-zeros can be recovered computationally efficiently from only n random projections with n=2e k log(N/n), or that for a surprisingly large set of optimization problems the feasible set is actually a point. These implications are driving a new signal processing paradigm, Compressed Sensing, which has already lead to substantive improvements in various imaging modalities. This work is joint with David L. Donoho.
  • Stochastic Analysis Seminar