Almost Euclidean subspaces of ℓ 1 N VIA expander codes
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Through known connections between such Euclidean sections of ℓ1 and compressed sensing matrices, our result also gives explicit compressed sensing matrices for low compression factors for which basis pursuit is guaranteed to recover sparse signals. Our construction makes use of unbalanced bipartite graphs to impose local linear constraints on vectors in the subspace, and our analysis relies on expansion properties of the graph. This is inspired by similar constructions of error-correcting codes.
Mathematics Subject Classification (2000)68R05 68P30 51N20
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