Random projections of regular simplices
Discrete & Computational Geometry
Weighted l1 minimization for sparse recovery with prior information
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On sharp performance bounds for robust sparse signal recoveries
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Decoding by linear programming
IEEE Transactions on Information Theory
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It is now well understood that l1 minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the l1 minimization algorithm. In this paper, we investigate a new iterative reweighted l1 minimization algorithm and showed that the new algorithm can increase the sparsity recovery threshold of l1 minimization when decoding signals from relevant distributions. Interestingly, we observed that the recovery threshold performance of the new algorithm depends on the behavior, more specifically the derivatives, of the signal amplitude probability distribution at the origin.