On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes
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| Ngôn ngữ: | English |
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s11590-022-01927-0 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7409 |
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oai:localhost:PNK-74092023-04-03T03:31:54Z On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes Abdullah, Alasmari Iskander, Aliev maximum absolute entry Δ=O(r2l−1) exponent 2l−1 CC BY 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(r2l−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. 2023-04-03T02:12:24Z 2023-04-03T02:12:24Z 2022 Book https://link.springer.com/article/10.1007/s11590-022-01927-0 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7409 en application/pdf Springer |
| institution |
Digital Phenikaa |
| collection |
Digital Phenikaa |
| language |
English |
| topic |
maximum absolute entry Δ=O(r2l−1) exponent 2l−1 |
| spellingShingle |
maximum absolute entry Δ=O(r2l−1) exponent 2l−1 Abdullah, Alasmari Iskander, Aliev On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes |
| description |
CC BY |
| format |
Book |
| author |
Abdullah, Alasmari Iskander, Aliev |
| author_facet |
Abdullah, Alasmari Iskander, Aliev |
| author_sort |
Abdullah, Alasmari |
| title |
On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes |
| title_short |
On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes |
| title_full |
On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes |
| title_fullStr |
On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes |
| title_full_unstemmed |
On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes |
| title_sort |
on unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes |
| publisher |
Springer |
| publishDate |
2023 |
| url |
https://link.springer.com/article/10.1007/s11590-022-01927-0 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7409 |
| _version_ |
1762184301082836992 |
| score |
8.893527 |