Verifiable conditions of ℓ1-recovery for sparse signals with sign restrictions
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We propose necessary and sufficient conditions for a sensing matrix to be “s-semigood” – to allow for exact ℓ1-recovery of sparse signals with at most s nonzero entries under sign restrictions on part of the entries. We express error bounds for imperfect ℓ1-recovery in terms of the characteristics underlying these conditions. These characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse ℓ1-recovery and thus efficiently computable upper bounds on those s for which a given sensing matrix is s-semigood. We examine the properties of proposed verifiable sufficient conditions, describe their limits of performance and provide numerical examples comparing them with other verifiable conditions from the literature.
Mathematics Subject Classification (2000)90C90 90C05 90C22 62J05
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