TY - GEN

T1 - Support recovery with sparsely sampled free random matrices

AU - Tulino, Antonia

AU - Caire, Giuseppe

AU - Shamai, Shlomo

AU - Verdu, Sergio

PY - 2011

Y1 - 2011

N2 - Consider a Bernoulli-Gaussian complex n-vector whose components are X iBi, with Bi ∼Bernoulli-q and Xi ∼CN(0; σ2), iid across i and mutually independent. This random q-sparse vector is multiplied by a random matrix U, and a randomly chosen subset of the components of average size np, p ∈[0; 1], of the resulting vector is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where U is typically the identity or a matrix with iid components, to allow U that satisfies a certain freeness condition, which encompasses Haar matrices and other unitarily invariant matrices. We use the replica method and the decoupling principle of Guo and Verdú, as well as a number of information theoretic bounds, to study the input-output mutual information and the support recovery error rate as n→∞.

AB - Consider a Bernoulli-Gaussian complex n-vector whose components are X iBi, with Bi ∼Bernoulli-q and Xi ∼CN(0; σ2), iid across i and mutually independent. This random q-sparse vector is multiplied by a random matrix U, and a randomly chosen subset of the components of average size np, p ∈[0; 1], of the resulting vector is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where U is typically the identity or a matrix with iid components, to allow U that satisfies a certain freeness condition, which encompasses Haar matrices and other unitarily invariant matrices. We use the replica method and the decoupling principle of Guo and Verdú, as well as a number of information theoretic bounds, to study the input-output mutual information and the support recovery error rate as n→∞.

KW - Compressed Sensing

KW - Random Matrices

KW - Rate-Distortion Theory

KW - Sparse Models

KW - Support Recovery

UR - http://www.scopus.com/inward/record.url?scp=80054818160&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054818160&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6033978

DO - 10.1109/ISIT.2011.6033978

M3 - Conference contribution

AN - SCOPUS:80054818160

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2328

EP - 2332

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

Y2 - 31 July 2011 through 5 August 2011

ER -