On exact recovery of sparse vectors from linear measurements |
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Authors: | S V Konyagin Yu V Malykhin K S Ryutin |
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Institution: | 1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia 2. Moscow State University, Moscow, Russia
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Abstract: | Let 1 ≤ k ≤ n < N. We say that a vector x ∈ ? N is k-sparse if it has at most k nonzero coordinates. Let Φ be an n × N matrix. We consider the problem of recovery of a k-sparse vector x ∈ ? N from the vector y = Φx ∈ ? n . We obtain almost-sharp necessary conditions for k, n, N for this problem to be reduced to that of minimization of the ?1-norm of vectors z satisfying the condition y = Φz. |
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