Number of measurements in sparse signal recovery

Authors:
Paul Tune;Sibi Raj Bhaskaran;Stephen Hanly
Affiliations:
University of Melbourne, VIC, Australia;University of Melbourne, VIC, Australia;University of Melbourne, VIC, Australia
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Year:
2009

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Abstract

We analyze the asymptotic performance of sparse signal recovery from noisy measurements. In particular, we generalize some of the existing results for the Gaussian case to subgaussian and other ensembles. An achievable result is presented for the linear sparsity regime. A converse on the number of required measurements in the sub-linear regime is also presented, which cover many of the widely used measurement ensembles. Our converse idea makes use of a correspondence between compressed sensing ideas and compound channels in information theory.