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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Official URL: https://doi.org/10.1007/s11590-022-01927-0
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 |
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| Date Type: | Published Online |
| Status: | Published |
| Schools: | 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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