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arXiv · 1410.6457

A conditional construction of restricted isometries

Afonso S. Bandeira·Dustin G. Mixon·Joel Moreira
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Abstract

We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an $ε>0$ such that, conditioned on a folklore conjecture in number theory, this matrix satisfies the restricted isometry property with sparsity parameter $K=Ω(M^{1/2+ε})$, where $M$ is the number of rows.

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BibTeXRIS

Afonso S. Bandeira, Dustin G. Mixon, Joel Moreira. 2014-10-23. A conditional construction of restricted isometries. https://arxiv.org/abs/1410.6457

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