Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of regression vector or noise statistics. Both these statistics are rarely known \textit{a priori} and are very difficult to estimate. In this paper, we present a novel technique called residual ratio thresholding (RRT) to operate OMP without any \textit{a priori} knowledge of sparsity and noise statistics and establish finite sample and large sample support recovery guarantees for the same. Both analytical results and numerical simulations in real and synthetic data sets indicate that RRT has a performance comparable to OMP with \textit{a priori} knowledge of sparsity and noise statistics.

本篇论文提出了一种名为残差比阈值法（Residual Ratio Thresholding，RRT）的新技术，可以在没有关于疏密性和噪声统计的任何先验知识情况下运行正交匹配追踪（Orthogonal Matching Pursuit，OMP），并为其建立有限样本和大样本支持恢复保证。分析结果和实数及虚数数据集的数值模拟表明，RRT 的性能与具有先验知识的 OMP 相当。

信号和噪音统计信息不可知的正交匹配追踪