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On unique recovery of finite‑valued integer signals and admissible lattices of sparse hypercubes

Alasmari, Abdullah and Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207 2022. On unique recovery of finite‑valued integer signals and admissible lattices of sparse hypercubes. Optimization Letters 10.1007/s11590-022-01927-0

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Abstract

The paper considers the problem of unique recovery of sparse finite-valued integer signals using a single linear integer measurement. For l-sparse signals in ℤn, 2l < n, with absolute entries bounded by r, we construct an 1 × n measurement matrix with maximum absolute entry Δ = O(r^(2l−1)). Here the implicit constant depends on l and n and the exponent 2l − 1 is optimal. Additionally, we show that, in the above setting, a single measurement can be replaced by several measurements with absolute entries sub-linear in Δ. The proofs make use of results on admissible (n − 1)-dimensional integer lattices for m-sparse n-cubes that are of independent interest.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 1862-4472
Date of First Compliant Deposit: 28 September 2022
Date of Acceptance: 20 August 2022
Last Modified: 23 May 2023 00:44
URI: https://orca.cardiff.ac.uk/id/eprint/152934

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