New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property

@article{Krahmer2011NewAI,
  title={New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property},
  author={Felix Krahmer and Rachel Ward},
  journal={SIAM J. Math. Analysis},
  year={2011},
  volume={43},
  pages={1269-1281}
}
The Johnson-Lindenstrauss (JL) Lemma states that any set of p points in high dimensional Euclidean space can be embedded into O(δ−2 log(p)) dimensions, without distorting the distance between any two points by more than a factor between 1 − δ and 1 + δ . We establish a new connection between the JL Lemma and the Restricted Isometry Property (RIP), a well-known concept in the theory of sparse recovery often used for showing the success of `1-minimization. Consider an m×N matrix satisfying the (k… CONTINUE READING
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