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 ∈ > 0 such that, conditioned on a folklore conjecture in number theory, this matrix satisfies the restricted isometry property with sparsity parameter K = Ω(M1/2+∈), where M is the number of rows.

Original languageEnglish (US)
Pages (from-to)372-381
Number of pages10
JournalInternational Mathematics Research Notices
Volume2017
Issue number2
DOIs
StatePublished - Jan 1 2017

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ASJC Scopus subject areas

  • Mathematics(all)

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