|Stochastic Systems Group|
The Geometry of Compressive Sensing
Michael B. Wakin
University of Michigan
Compressive Sensing (CS) is a rapidly emerging field based on the revelation that signals obeying sparse models can be recovered from small numbers of nonadaptive (even random) linear measurements. In this talk I will survey some of the theoretical foundations of CS, highlighting the important role that geometry has played in the development of the core CS theory and exploring new directions in signal processing that have been inspired by this perspective. I will demonstrate how visual, geometric arguments can lead to a clear, intuitive understanding of the reasons why sparse signals can be recovered from random projections, and I will emphasize connections between a broad variety of geometric themes, including convex optimization, Uniform Uncertainty Principles, the Johnson-Lindenstrauss lemma, and Whitney's embedding theorem for manifolds. Following on recent results for random projections of manifold-modeled signals, I will also discuss new applications in multi-signal CS.
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