Compressed sensing with support information

Start: 11/05/2014 - 4:15pm
End  : 11/05/2014 - 5:15pm


Rayan Saab, University of California, San Diego


Compressed sensing is a signal acquisition paradigm that utilizes the sparsity of a signal (a vector in $ \mathbb{R}^N $ with $ s $ << $ N $ non-zero entries) to efficiently reconstruct it from very few (say $ m $, where $ s $ <$ m $ << $ N $) generalized linear measurements. These measurements often take the form of inner products with random vectors drawn from appropriate distributions, and the reconstruction is typically done using convex optimization algorithms or computationally efficient greedy algorithms.

We discuss compressed sensing under the additional, and often practical, assumption that we have some estimate of the support-albeit this estimate is not fully accurate.
In this setting, we discuss using weighted $ \ell_1 $ minimization as a reconstruction method. We give reconstruction guarantees that improve on the standard results when the support information is accurate enough and when the weights are chosen correctly.

Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

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