论文标题
自然阈值算法用于信号恢复的稀疏性
Natural Thresholding Algorithms for Signal Recovery with Sparsity
论文作者
论文摘要
最近提出了基于最佳$ k $ thesholding（OT）技术的算法以进行信号恢复，它们与传统的硬阈值方法的传统家族大不相同。但是，基于OT的算法的计算成本在其开发的当前阶段仍然很高。这刺激了本文所谓的自然阈值（NT）算法的发展及其变体。 NT算法家族是通过所谓的正规$ k $ thines持有模型的一阶近似开发的，因此该算法家族的计算成本大大低于基于OT的算法的计算成本。从噪声测量值中显示了NT型算法用于信号恢复的NT型算法的保证性能在受限的等轴测属性和正规化最佳$ K $ thresholding模型的目标函数的凹度下显示。经验结果表明，NT型算法具有鲁棒性，并且与几种主流算法相当，可用于稀疏信号恢复。
The algorithms based on the technique of optimal $k$-thresholding (OT) were recently proposed for signal recovery, and they are very different from the traditional family of hard thresholding methods. However, the computational cost for OT-based algorithms remains high at the current stage of their development. This stimulates the development of the so-called natural thresholding (NT) algorithm and its variants in this paper. The family of NT algorithms is developed through the first-order approximation of the so-called regularized optimal $k$-thresholding model, and thus the computational cost for this family of algorithms is significantly lower than that of the OT-based algorithms. The guaranteed performance of NT-type algorithms for signal recovery from noisy measurements is shown under the restricted isometry property and concavity of the objective function of regularized optimal $k$-thresholding model. Empirical results indicate that the NT-type algorithms are robust and very comparable to several mainstream algorithms for sparse signal recovery.
