Sparse Signal Recovery from Random Measurements
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 $Θ(\log n)$ 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.
Fields of Study & Subjects
Sparse and Compressive Sensing Techniques
Mathematical Analysis and Transform Methods
Numerical methods in inverse problems
Publication details
- Journal / source
- IEEE International Symposium on Information Theory (ISIT)
- Pages
- 1–6
- Publication date
- 1 June 2026
- Language
- EN