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 \(k = \Omega( n^{1/2+\varepsilon/4)}\).
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The first author was partially supported by NSF Grant DMS-1802139.
The second author is supported by a Simons Travel grant.
The third author is supported by Ben Green’s Simons Investigator Grant 376201.
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Ford, K., Kutzarova, D. & Shakan, G. Explicit RIP matrices: an update. Acta Math. Hungar. 168, 509–515 (2022). https://doi.org/10.1007/s10474-022-01290-7
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DOI: https://doi.org/10.1007/s10474-022-01290-7