Abstract
In this paper, we study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent entries, we prove that the partial random circulant matrices satisfy s-order RIP with high probability if one chooses m ≳ s log2 s log n rows randomly where n is the vector length. This improves the previously known bound m ≳ s log2 s log2 n.
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