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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.10569 |
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| _version_ | 1866918291543425024 |
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| author | Wong, Man Ting Cheng, Siu-Wing |
| author_facet | Wong, Man Ting Cheng, Siu-Wing |
| contents | Given the compressed sensing measurements of an unknown vector $z \in \mathbb{R}^n$ using random matrices, we present a simple method to determine $z$ without solving any optimization problem or linear system. Our method uses $Θ(\log n)$ random sensing matrices in $\mathbb{R}^{k \times n}$ and runs in $O(kn\log n)$ time, where $k = Θ(s\log n)$ and $s$ is the number of nonzero coordinates in $z$. We adapt our method to determine the support set of $z$ and experimentally compare with some optimization-based methods on binary signals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10569 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sparse Signal Recovery from Random Measurements Wong, Man Ting Cheng, Siu-Wing Information Theory Given the compressed sensing measurements of an unknown vector $z \in \mathbb{R}^n$ using random matrices, we present a simple method to determine $z$ without solving any optimization problem or linear system. Our method uses $Θ(\log n)$ random sensing matrices in $\mathbb{R}^{k \times n}$ and runs in $O(kn\log n)$ time, where $k = Θ(s\log n)$ and $s$ is the number of nonzero coordinates in $z$. We adapt our method to determine the support set of $z$ and experimentally compare with some optimization-based methods on binary signals. |
| title | Sparse Signal Recovery from Random Measurements |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.10569 |