论文标题
通过一声硬阈值进行一次性压缩感测
One-Bit Compressed Sensing via One-Shot Hard Thresholding
论文作者
论文摘要
本文涉及1位压缩传感的问题，目的是估算其一些二进制测量值的稀疏信号。我们研究了一个非凸线稀疏限制的程序，并提出了一种新颖而简洁的分析，该分析远离了高斯宽度的广泛使用概念。我们表明，使用高概率，可以保证，在$ \ ell_2 $ - metric下，一种简单的算法可以准确地近似于归一化感兴趣的信号。最重要的是，我们建立了一个新的结果集合，以解决规范估计，支持恢复和模型错误指定。在计算方面，可以证明可以通过一步硬阈值解决非凸线程序，这在时间复杂性和内存足迹方面在很大程度上有效。在统计方面，显示我们的估计器在标准条件下的误差率近乎最佳。理论结果通过数值实验证实。
This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis that moves away from the widely used notion of Gaussian width. We show that with high probability a simple algorithm is guaranteed to produce an accurate approximation to the normalized signal of interest under the $\ell_2$-metric. On top of that, we establish an ensemble of new results that address norm estimation, support recovery, and model misspecification. On the computational side, it is shown that the non-convex program can be solved via one-step hard thresholding which is dramatically efficient in terms of time complexity and memory footprint. On the statistical side, it is shown that our estimator enjoys a near-optimal error rate under standard conditions. The theoretical results are substantiated by numerical experiments.
