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A matrix $\Phi \in \mathbb{R}^{Q \times N}$ satisfies the restricted isometryproperty 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. Themain technical ingredient is an extension of the Hanson-Wright inequality to$\epsilon$-biased distributions.

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