论文标题
从结构化偏置测量中恢复二进制稀疏信号
Recovery of Binary Sparse Signals from Structured Biased Measurements
论文作者
论文摘要
在本文中，我们研究了部分随机循环测量值的二进制稀疏信号的重建。我们表明，通过最小二乘算法的重建与通常使用的程序基础追求的重建一样好。我们进一步表明，我们需要尽可能多的测量来恢复$ s -sparse信号$ x_0 \ in \ mathbb {r}^n $，因为我们需要恢复一个密集信号，更准确地是$ n-s $ -s-sparse Signal $ x_0 \ in \ mathbb {r}^n $。我们进一步建立了有关嘈杂测量的稳定性。
In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program basis pursuit. We further show that we need as many measurements to recover an $s$-sparse signal $x_0\in\mathbb{R}^N$ as we need to recover a dense signal, more-precisely an $N-s$-sparse signal $x_0\in\mathbb{R}^N$. We further establish stability with respect to noisy measurements.
