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压缩感知中非凸优化的极大熵方法
引用本文:王天荆,杨震,郑宝玉.压缩感知中非凸优化的极大熵方法[J].工程数学学报,2012,29(3):451-461.
作者姓名:王天荆  杨震  郑宝玉
作者单位:1. 南京邮电大学电子科学与工程学院,南京210003;南京工业大学理学院,南京210009
2. 南京邮电大学电子科学与工程学院,南京,210003
基金项目: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.

关 键 词:非凸优化  非光滑优化  同伦方法  极大熵方法

Maximum Entropy Function Method for Nonconvex Optimization in Compressed Sensing
WANG Tian-jing , YANG Zhen , ZHENG Bao-yu.Maximum Entropy Function Method for Nonconvex Optimization in Compressed Sensing[J].Chinese Journal of Engineering Mathematics,2012,29(3):451-461.
Authors:WANG Tian-jing  YANG Zhen  ZHENG Bao-yu
Affiliation:1(1-College of Electronic Science and Engineering,Nanjing University of Posts and Telecommunications,Nanjing 210003;2-College of Sciences,Nanjing University of Technology,Nanjing 210009)
Abstract:Compressed Sensing(CS) can reconstruct K-sparse signal from remarkably few measurements.The paper provides a new maximum entropy function(MEF) method to overcome the nonsmooth problem of the nonconvex l p(0 < p < 1) optimization in CS.MEF constructs a homotopy path to obtain the global optimal sparse solution.The numerical results show that MEF has better performance of signal reconstruction than the l 1 optimization and the affine scaling transformation algorithm.
Keywords:nonconvex optimization  nonsmooth optimization  homotopy method  maximum entropy function method
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