- Verifiable conditions of $\ell_1$-recovery for sparse signals with sign restrictions Anatoli Juditsky (juditskyimag.fr) Fatma Kilinc Karzan (fkilincgatech.edu) Arkadi Nemirovski (nemirovsisye.gatech.edu) Abstract: We propose necessary and sufficient conditions for a sensing matrix to be $s$-semigood'' -- to allow for exact $\ell_1$-recovery of sparse signals with at most $s$ nonzero entries under sign restrictions on part of the entries. We express error bounds for imperfect $\ell_1$-recovery in terms of the characteristics underlying these conditions. These characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse $\ell_1$-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. Keywords: compressive sensing, sparse recovery Category 1: Applications -- Science and Engineering (Statistics ) Citation: Download: [PDF]Entry Submitted: 03/31/2009Entry Accepted: 03/31/2009Entry Last Modified: 09/22/2010Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society.