Sharp Sufficient Conditions on Exact Sparsity Pattern Recovery
نویسنده
چکیده
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 drawn from a Gaussian ensemble, we obtain asymptotically sharp sufficient conditions for exact recovery, which agree with the known necessary conditions previously established.
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