Necessary and Sufficient Conditions for Sparsity Pattern Recovery
نویسندگان
چکیده
منابع مشابه
Necessary and Sufficient Conditions on Sparsity Pattern Recovery
The problem of detecting the sparsity pattern of a k-sparse vector in Rn from m random noisy measurements is of interest in many areas such as system identification, denoising, pattern recognition, and compressed sensing. This paper addresses the scaling of the number of measurements m, with signal dimension n and sparsity-level nonzeros k, for asymptotically-reliable detection. We show a neces...
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Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...
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Consider the n-dimensional vector y = Xβ+ ǫ, where β ∈ R has only k nonzero entries and ǫ ∈ R is a Gaussian noise. This can be viewed as a linear system with sparsity constraints, corrupted by noise. We find a non-asymptotic upper bound on the probability that the optimal decoder for β declares a wrong sparsity pattern, given any generic perturbation matrix X . In the case when X is randomly dr...
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The theory of compressed sensing shows that sparsity pattern (or support) of a sparse signal can be recovered from a small number of appropriate linear projections (samples). Unfortunately, as soon as noise is added, the number of required samples exceeds the full signal dimension, rendering compressed sensing ineffective. In recent work, we have shown that this can be fixed if a small distorti...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2009
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2009.2032726