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

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Main Authors: Abdullah, Alasmari, Iskander, Aliev
Format: Book
Language:English
Published: Springer 2023
Subjects:
maximum absolute entry Δ=O(r2l−1)
exponent 2l−1
Online Access:https://link.springer.com/article/10.1007/s11590-022-01927-0
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7409
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spelling 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 8.891145

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