Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the sparse signal recovery problem. More recently, Natural Thresholding (NT) has been proposed with improved computational efficiency. This paper proposes and discusses convergence guarantees for stochastic natural thresholding algorithms by extending the NT from the deterministic version with linear measurements to the stochastic version with a general objective function. We also conduct various numerical experiments on linear and nonlinear measurements to demonstrate the performance of StoNT.

翻译：稀疏信号恢复是医学成像和遥感等多种应用中最基本的问题之一。基于硬阈值算子族的许多贪心算法已被开发用于解决稀疏信号恢复问题。近期，自然阈值法（Natural Thresholding, NT）被提出并提升了计算效率。本文将自然阈值法从基于线性测量的确定性版本扩展到具有一般目标函数的随机版本，提出并讨论了随机自然阈值算法的收敛性保证。我们还在线性和非线性测量上进行了多种数值实验，以验证随机自然阈值算法（StoNT）的性能。