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support_recovery_with_sparsely_sampled_free_random_matrices

Abstract: Consider a Bernoulli-Gaussian complex n-vector whose components are V_{i}=X_{i}B_{i}, with V_{i} ~ CN(0,P_{x}) and B_{i} mutually independent and iid across i. This random q-sparse vector is multiplied by a square random matrix U, and a randomly chosen subset, of average size np, p ∈ [0, 1], of the resulting vector components is then observed in additive Gaussian noise.

In this talk we extend the scope of conventional noisy compressive sampling models where U is typically a matrix with iid components, to allow U satisfying a certain freeness condition. This class of matrices 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 in the limit of n → ∞. We also extend the scope of the large deviation approach of Rangan, Fletcher and Goyal and characterize the performance of a class of estimators encompassing thresholded linear MMSE and I relaxation.

Bio: Antonia M. Tulino (M'00-SM'05) received the Ph.D. degree from the Electrical Engineering Department, Seconda Universitá degli Studi di  Napoli, Italy, in 1999. She has served as Associate Professor at the Department of Electrical  and Telecommunications Engineering at the Universitá degli Studi di  Napoli “Federico II” since 2002. She is currently with the Department of Wireless Communications, Bell Laboratories, Alcatel-Lucent, Holmdel, NJ. She held research positions at the Center for Wireless Communications, Oulu, Finland and at the Department of Electrical  Engineering, Princeton University, Princeton, NJ. She has served on the Faculty of Engineering, Universitá degli Studi del Sannio, Benevento, Italy. Dr. Tulino has received the 2009 Stephen O. Rice Prize in the Field of Communications Theory for the best paper published in the IEEE TRANSACTION ON COMMUNICATIONS  in 2008. A frequent contributor to the IEEE TRANSACTIONS ON INFORMATION THEORY, the IEEE TRANSACTIONS ON COMMUNICATIONS, and the IEEE TRANSACTIONS ON SIGNAL PROCESSING, her research interests lay in the broad area of communication systems approached with the complementary tools provided by signal processing, information theory, and random matrix theory.

support_recovery_with_sparsely_sampled_free_random_matrices.txt · Last modified: 2016/09/01 19:15 (external edit)