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- W2924908021 abstract "Let $A$ be an $N times N$ Fourier matrix over $mathbb{F}_p^{log{N}/log{p}}$ for some prime $p$. We improve upon known lower bounds for the number of rows of $A$ that must be sampled so that the resulting matrix $M$ satisfies the restricted isometry property for $k$-sparse vectors. This property states that $|Mv|_2^2$ is approximately $|v|_2^2$ for all $k$-sparse vectors $v$. In particular, if $k = Omega( log^2{N})$, we show that $Omega(klog{k}log{N}/log{p})$ rows must be sampled to satisfy the restricted isometry property with constant probability." @default.
- W2924908021 created "2019-04-01" @default.
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- W2924908021 date "2019-03-28" @default.
- W2924908021 modified "2023-09-27" @default.
- W2924908021 title "Improved Lower Bounds for the Restricted Isometry Property of Subsampled Fourier Matrices." @default.
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