Verifiable Conditions of L1-recovery of Sparse Signals with Sign Restriction

We propose necessary&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. We express error bounds for imperfect L1-recovery in terms of these characteristics. These, despite being difficult to evaluate, lead to verifiable sufficient conditions and efficiently computable upper bounds on those s for which a given matrix is s-semigood.We study their properties and limits of performance.