Sparse Signal Recovery from Random Measurements
🤖 AI Summary
This work addresses the problem of efficiently recovering sparse signals from random compressive measurements without solving optimization problems or linear systems. The authors propose a novel method that utilizes only Θ(log n) random sensing matrices to accurately recover the support set and reconstruct the signal in O(kn log n) time, where k = Θ(s log n) and s denotes the number of non-zero entries. To the best of the authors’ knowledge, this is the first approach to achieve efficient sparse recovery without relying on optimization or linear system solvers. Experimental results on binary signals demonstrate the effectiveness of the proposed method, showing superior performance compared to several existing optimization-based algorithms.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Sparse Signal Recovery
Compressed Sensing
Random Measurements
Support Recovery
Binary Signals
Innovation
Methods, ideas, or system contributions that make the work stand out.
Sparse Signal Recovery
Compressed Sensing
Random Measurements
Support Recovery
Optimization-Free Algorithm
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