A Simple Proof for Recoverability of `1-Minimization (II): the Nonnegativity Case
نویسنده
چکیده
When using `1 minimization to recover a sparse, nonnegative solution to a underdetermined linear system of equations, what is the highest sparsity level at which recovery can still be guaranteed? Recently, Donoho and Tanner [10] discovered, by invoking classic results from the theory of convex polytopes [11, 12], that the highest sparsity level equals half of the number of equations. In this paper, we connect dots for different recoverability conditions obtained from different spaces, and provide an alternative, self-contained and elementary proof for this remarkable result.
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