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CORR
2008
Springer

Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices

10 years 4 months ago
Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices
We study the information-theoretic limits of exactly recovering the support set of a sparse signal, using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of observations n, the ambient signal dimension p, and the signal sparsity k are all allowed to tend to infinity in a general manner. This paper makes two novel contributions. First, we provide sharper necessary conditions for exact support recovery using general (including non-Gaussian) dense measurement matrices. Combined with previously known sufficient conditions, this result yields sharp characterizations of when the optimal decoder can recover a signal for various scalings of the signal sparsity k and sample size n, including the important special case of linear sparsity (k = 2(p)) using a linear scaling of observations (n = 2(p)). Our second contribution is to prove necessary conditions on the number of observations n required for asymptotical...
Wei Wang, Martin J. Wainwright, Kannan Ramchandran
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Wei Wang, Martin J. Wainwright, Kannan Ramchandran
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