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ICASSP
2009
IEEE

On the recovery of nonnegative sparse vectors from sparse measurements inspired by expanders

9 years 7 months ago
On the recovery of nonnegative sparse vectors from sparse measurements inspired by expanders
This paper studies compressed sensing for the recovery of non-negative sparse vectors from a smaller number of measurements than the ambient dimension of the unknown vector. We focus on measurement matrices that are sparse, i.e., have only a constant number of nonzero (and non-negative) entries in each column. For such measurement matrices we give a simple necessary and sufficient condition for l1 optimization to successfully recover the unknown vector. Using a simple "perturbation" to the adjacency matrix of an unbalanced expander, we obtain simple closed form expressions for the threshold relating the ambient dimension n, number of measurements m and sparsity level k, for which l1 optimization is successful with overwhelming probability. Simulation results suggest that the theoretical thresholds are fairly tight and demonstrate that the "perturbations" significantly improve the performance over a direct use of the adjacency matrix of an expander graph.
M. Amin Khajehnejad, Babak Hassibi
Added 18 Feb 2011
Updated 18 Feb 2011
Type Journal
Year 2009
Where ICASSP
Authors M. Amin Khajehnejad, Babak Hassibi
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