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Sparse recovery under weak moment assumptions

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      Abstract

      We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible estimate -- exhibited by a random gaussian matrix. We also prove that this moment condition is necessary, up to a \(\log \log \) factor. Applications to the Compatibility Condition and the Restricted Eigenvalue Condition in the noisy setup and to properties of neighbourly random polytopes are also discussed.

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      Journal
      2014-01-09
      2015-03-03
      1401.2188

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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      math.ST math.PR stat.TH

      Probability, Statistics theory

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