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

Preview

PDF - Published Version Available under License Creative Commons Attribution. Download (1MB) | Preview

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

Actions (repository staff only)

Edit Item