基于SCAD的压缩感知阈值迭代算法的收敛性分析  

Convergence Analysis of Compressive Sensing Based on SCAD Iterative Thresholding Algorithm

作　　者：张会[1] 张海[1,2] 勾明 

机构地区：[1]西北大学数学学院,西安710069 [2]中国科学院数学与系统科学研究院应用数学研究所,北京100190

出　　处：《工程数学学报》2016年第3期243-258,共16页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11171272;11571011);陕西省自然科学基金(2011JM1008);陕西省教育厅专项科研计划(JC11217)~~

摘　　要：基于SCAD罚函数的压缩感知在有噪声稀疏信号重建中具有优良的理论及应用效果,开展其快速重建算法研究有着重要的意义,阈值迭代算法是解决压缩传感问题最有效的算法之一.本文研究了基于SCAD罚函数的压缩感知阈值迭代算法的收敛性问题,给出了算法收敛到稀疏解的充分条件,并证明了迭代估计值以指数阶速率收敛于最优值.进一步,本文给出了基于AMP改进的SCAD阈值迭代算法的收敛性分析.Compressive sensing based on SCAD has good theoretical properties for sparse signal reconstruction with noise. It is vital to study this kind of algorithms. The iterative thresholding algorithm is one of the most efficient algorithms to solve the problem of compressed sensing. In this paper, we study the convergence of the iterative thresholding algorithm for compressive sensing based on SCAD. We give some sufficient conditions on the convergence of the iterative thresholding algorithm. We prove that the algorithm is convergent with exponentially decaying error. Furthermore, we study the convergence of an improved iterative thresholding SCAD algorithm based on an approximate message passing algorithm.

关 键 词：压缩感知 SCAD 阈值迭代算法 稀疏性 

分 类 号：O175.29[理学—数学]