Sparse Signal Recovery from Random Measurements

Man Ting Wong; Siu-Wing Cheng

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arXiv · 2601.10569

Sparse Signal Recovery from Random Measurements

Man Ting Wong·Siu-Wing Cheng

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Abstract

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 $\Theta(\log n)$ random sensing matrices in $\mathbb{R}^{k \times n}$ and runs in $O(kn\log n)$ time, where $k = \Theta(s\log n)$ 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.

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Man Ting Wong, Siu-Wing Cheng. 2026-01-15. Sparse Signal Recovery from Random Measurements. https://arxiv.org/abs/2601.10569

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