A Simple Proof for Recoverability of L1-Minimization: Go Over or Under?
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It is well-known by now that L1 minimization can help recover sparse solutions to under-determined linear equations or sparsely corrupted solutions to over-determined equations, and the two problems are equivalent under appropriate conditions. So far almost all theoretic results have been obtained through studying the under-determined side'' of the problem. In this note, we take a different approach from the
over-determined side'' and show that a recoverability result (with the best available order) follows almost immediately from an inequality of Garnaev and Gluskin. We also connect dots with recoverability conditions obtained from different spaces.
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Zhang, Yin. "A Simple Proof for Recoverability of L1-Minimization: Go Over or Under?." (2005) https://hdl.handle.net/1911/102040.