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Explicit RIP matrices: an update (2108.01794v3)
Published 4 Aug 2021 in math.CO, cs.IT, and math.IT
Abstract: Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better parameters. Namely, for $\varepsilon=3.26\cdot 10{-7}$, large $k$ and $k{2-\varepsilon} \le N\le k{2+\varepsilon}$, we construct $n \times N$ RIP matrices of order $k$ with $k = \Omega( n{1/2+\varepsilon/4} )$.