The Johnson-Lindenstrauss Lemma Meets Compressed Sensing

  title={The Johnson-Lindenstrauss Lemma Meets Compressed Sensing},
  author={Richard G. Baraniuk and Mark A. Davenport and Ronald A. DeVore and Michael B. Wakin},
We show how two fundamental results in analysis related to n-widths and Compressed Sensing are intimately related to the Johnson-Lindenstrauss lemma. Our elementary approach is based on the same concentration inequalities for random inner products that have recently provided simple proofs of the Johnson-Lindenstrauss lemma. We show how these ideas lead to simple proofs of Kashin’s theorems on widths of finite balls in Euclidean space (and their improvements due to Gluskin) as well as the… CONTINUE READING
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