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 -