Abstract One important task in signal processing is to construct effective algorithms to reconstruct sparse signals from an underdetermined system of linear equations. In this paper, we propose a new sparse recovery algorithm called multipath least squares (MLS), which investigates multiple promising candidates per step and parallels the multipath matching pursuit (MMP) algorithm in this aspect. The performance of the MLS algorithm is evaluated through the ability of signal recovery. Specifically, a recovery guarantee based on the restricted isometry property (RIP) is established for MLS that ensures its exact recovery of any K-sparse signal x from the measurements y = Ax . It is also shown that this sufficient condition is nearly sharp by providing a counterexample such that the algorithm may fail to recover some K-sparse signal. Moreover, the recovery guarantee of the MLS algorithm is also provided for the case of noisy measurements. Finally, numerical experiments are conducted to demonstrate the validity and priority of the proposed algorithm.

中文翻译：

---

多径最小二乘算法与分析

摘要 信号处理中的一项重要任务是构建有效的算法，从欠定的线性方程组重建稀疏信号。在本文中，我们提出了一种称为多路径最小二乘法 (MLS) 的新稀疏恢复算法，该算法每步研究多个有希望的候选者，并在这方面与多路径匹配追踪 (MMP) 算法并行。MLS算法的性能通过信号恢复的能力来评估。具体而言，为 MLS 建立了基于受限等距特性 (RIP) 的恢复保证，以确保其从测量值 y = Ax 中准确恢复任何 K 稀疏信号 x。还通过提供一个反例表明该充分条件几乎是尖锐的，使得算法可能无法恢复一些 K 稀疏信号。而且，对于噪声测量的情况，也提供了 MLS 算法的恢复保证。最后，通过数值实验证明了所提出算法的有效性和优先级。