TY - GEN
T1 - The restricted isometry property of subsampled Fourier matrices
AU - Haviv, Ishay
AU - Regev, Oded
PY - 2016
Y1 - 2016
N2 - A matrix A ∈ Cq×N satisfies the restricted isometry property of order k with constant e if it preserves the l2 norm of all κ-sparse vectors up to a factor of 1 ± ϵ. We prove that a matrix A obtained by randomly sampling q = O(k· log2 k · log TV) rows from an N × N Fourier matrix satisfies the restricted isometry property of order k with a fixed e with high probability. This improves on Rudelson and Vershynin (Comm. Pure Appl. Math., 2008), its subsequent improvements, and Bourgain (GAFA Seminar Notes, 2014).
AB - A matrix A ∈ Cq×N satisfies the restricted isometry property of order k with constant e if it preserves the l2 norm of all κ-sparse vectors up to a factor of 1 ± ϵ. We prove that a matrix A obtained by randomly sampling q = O(k· log2 k · log TV) rows from an N × N Fourier matrix satisfies the restricted isometry property of order k with a fixed e with high probability. This improves on Rudelson and Vershynin (Comm. Pure Appl. Math., 2008), its subsequent improvements, and Bourgain (GAFA Seminar Notes, 2014).
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U2 - 10.1137/1.9781611974331.ch22
DO - 10.1137/1.9781611974331.ch22
M3 - Conference contribution
AN - SCOPUS:84962826200
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 288
EP - 297
BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
A2 - Krauthgamer, Robert
PB - Association for Computing Machinery
T2 - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
Y2 - 10 January 2016 through 12 January 2016
ER -