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CORR
2007
Springer

Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting

13 years 11 months ago
Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting
The problem of recovering the sparsity pattern of a fixed but unknown vector β∗ ∈ Rp based on a set of n noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection, signal denoising, compressive sensing, and constructive approximation. Of interest are conditions on the model dimension p, the sparsity index s (number of non-zero entries in β∗ ), and the number of observations n that are necessary and/or sufficient to ensure asymptotically perfect recovery of the sparsity pattern. This paper focuses on the information-theoretic limits of sparsity recovery: in particular, for a noisy linear observation model based on measurement vectors drawn from the standard Gaussian ensemble, we derive both a set of sufficient conditions for asymptotically perfect recovery using the optimal decoder, as well as a set of necessary conditions that any decoder, regardless of its computational complexity, must satisfy for perfect recover...
Martin J. Wainwright
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where CORR
Authors Martin J. Wainwright
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