Satisfying the Restricted Isometry Property with the Optimal Number of Rows and Slightly Less Randomness

Shravas Rao

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arXiv · 2311.07889

Satisfying the Restricted Isometry Property with the Optimal Number of Rows and Slightly Less Randomness

Shravas Rao

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Abstract

A matrix $\Phi \in \mathbb{R}^{Q \times N}$ satisfies the restricted isometry property if $\|\Phi x\|_2^2$ is approximately equal to $\|x\|_2^2$ for all $k$-sparse vectors $x$. We give a construction of RIP matrices with the optimal $Q = O(k \log(N/k))$ rows using $O(k\log(N/k)\log(k))$ bits of randomness. The main technical ingredient is an extension of the Hanson-Wright inequality to $\epsilon$-biased distributions.

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Shravas Rao. 2023-11-14. Satisfying the Restricted Isometry Property with the Optimal Number of Rows and Slightly Less Randomness. https://arxiv.org/abs/2311.07889

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