脉冲噪声环境下基于洛伦兹范数软阈值迭代的压缩感知算法  

Lorentzian-Based Iterative Soft Threshold Algorithm for Compressed Sensing in the Presence of Impulsive Noise

作　　者：汪海兵 董天宝 竺小松 WANG Hai-bing, DONG Tian-bao,ZHU Xiao-song(Electronic Countermeasure Institute, National University of Defense Technology, Hefei 230037, Chin)

机构地区：[1]国防科技大学电子对抗学院,合肥230037

出　　处：《电子信息对抗技术》2018年第2期1-6,16,共7页Electronic Information Warfare Technology

基　　金：安徽省自然科学基金(1408085MF129)

摘　　要：观测值受脉冲噪声干扰情况下,传统的压缩感知算法基本失效,基于洛伦兹范数的硬阈值迭代(LIHT)算法是有效途径,但是硬阈值迭代过程会误判信号支撑集,随着脉冲数目增加,算法性能明显下降。针对这一问题,提出了一种基于洛伦兹范数的软阈值迭代(LIST)压缩感知重构算法。利用洛伦兹范数有效约束脉冲噪声,引入信号稀疏度度量函数,采用梯度下降法降低重构信号的稀疏度,实现软阈值迭代,并通过拟牛顿法求解该模型,加快算法收敛,运算量与其他算法是同一数量级,数值仿真表明,重构信噪比优于LIHT算法。In the presence of observation impulsive noise, the traditional compressed sensing re- construction algorithms usually fail, the Lorentzian-based iterative hard threshold （LIHT） algo- rithm is an effective way. However, the iterative hard threshold procedure misjudges the signal support set, and as the impulse number increases, the performance of the LIHT algorithm de- clines significantly. To handle this problem, a Lorentzian-based iterative soft threshold （LIST） compressed sensing reconstruction algorithm is proposed. The Lorentzian norm is employed to suppress the impulse noise effectively. The signal＇ s sparsity estimating function is introduced to reduce the reconstructed signal＇s sparsity via gradient descent procedure which is called the it- erative soft threshold （IST）. To speed up the convergence, the quasi-Newton method is ap- plied. The computation complexity is the same order of other algorithms. Numerical simulations show that the LIST algorithm outperforms the LIHT algorithm.

关 键 词：压缩感知 脉冲噪声 软阈值迭代 洛伦兹范数 拟牛顿方法 

分 类 号：TN971.1[电子电信—信号与信息处理]