### Simon Foucart (Pierre and Marie Curie University, Paris)

#### Compressive sensing via l_q-minimization for 0 < q <= 1

*Thursday 22 October 2009 at 13.00, JCMB 6206*

##### Abstract

After reviewing the use of l_1-minimization for the recovery of sparse vectors,
we investigate the advantages and drawbacks of substituting it by an
l_q-minimization for 0 < q < 1. On the theoretical side, we see that the
Restricted Isometry Condition guaranteeing recovery becomes weaker and that
the class of suitable random matrices becomes larger. On the algorithmic side,
we introduce an iteratively reweighted l_1-minimization scheme to approximate
the nonconvex l_q-minimization and we discuss its positive and negative
features.

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