压缩感知中非凸优化的极大熵方法(英文)  

Maximum Entropy Function Method for Nonconvex Optimization in Compressed Sensing

作　　者：王天荆[1,2] 杨震[1] 郑宝玉[1] 

机构地区：[1]南京邮电大学电子科学与工程学院,南京210003 [2]南京工业大学理学院,南京210009

出　　处：《工程数学学报》2012年第3期451-461,共11页Chinese Journal of Engineering Mathematics

基　　金：The Major State Basic Research Development Program(2011CB302903);the China Postdoctoral Science Foundation(20100481167);the National Natural Science Foundation of China(60971129);the Natural Science Foundation of Jiangsu Province(BK2011793);the Postdoctoral Science Foundation of Jiangsu Province(1101022B)

摘　　要：压缩感知可由少量观测重构K-稀疏信号.本文提出的极大熵方法克服了压缩感知中lp(0<p<1)最优化问题的非光滑性.极大熵方法构造一条同伦曲线以获得全局最优稀疏解.数值实验表明极大熵方法的信号重构性能优于l1最优化和AST算法.Compressed Sensing （CS） can reconstruct K-sparse signal from remarkably few measure- ments. The paper provides a new maximum entropy function （MEF） method to overcome the nonsmooth problem of the nonconvex Ip （0 〈 p 〈 1） optimization in CS. MEF con- structs a homotopy path to obtain the global optimal sparse solution. The numerical results show that MEF has better performance of signal reconstruction than the 11 optimization and the affine scaling transformation algorithm.

关 键 词：非凸优化 非光滑优化 同伦方法 极大熵方法 

分 类 号：TN912[电子电信—通信与信息系统]