|Stochastic Systems Group|
Compressed Sensing: Exact Asymptotic Bayesian Analysis and Other Stories
Prof. Vivek Goyal
The best-known results in compressed sensing are based on deterministic, worst-case measures such as the restricted isometry property. These results tend to be extremely conservative and predict performance that is far from what is actually observed experimentally. In this talk, I will present an alternative Bayesian analysis that is orders of magnitude sharper in the examples we have studied. For a large class of estimators, this methodology provides an exact asymptotic joint distribution between a signal component and its estimate. This facilitates computation of any performance criterion.
In addition, I will briefly describe ongoing work in exploiting sparsity in magnetic resonance imaging, optimizing quantizers in compressed sensing systems, and applying message passing algorithms to various estimation problems.
The talk is based on joint work with Sundeep Rangan, Alyson Fletcher, Daniel Weller, and John Sun.
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