压缩感知中信号重构的极大熵方法(英文)  

Maximum Entropy Function Method for Signal Reconstruction in Compressed Sensing

作　　者：王天荆[1] 杨震[2] 吴业军[3] 

机构地区：[1]南京工业大学理学院,江苏南京210009 [2]南京邮电大学信号与信息研究所,江苏南京210003 [3]南京工程学院基础部,江苏南京211167

出　　处：《应用数学》2010年第2期345-352,共8页Mathematica Applicata

基　　金：Supported by the National High Technology Research and Development Program of China (863 Project)(2006AA010102);the Young Teacher Academic Fund of Nanjing University of Technology

摘　　要：本文针对压缩感知理论中BP算法的l1最优化问题,构造了一种新的信号重构的极大熵方法.极大熵方法克服了l1最优化问题的非光滑性,同时根据同伦方法构造极大熵函数的最优解序列来逼近全局最优稀疏解.数值实验表明极大熵方法是十分有效的信号重构方法.The emerging theory of Compressed Sensing （CS） has led to the remarkable results that compressible signal can be reconstructed using only a small number of measurements.Significant attention in CS has been focused on Basis Pursuit （BP）,exchanging the sparseness constraint with the l1 norm.In order to overcome the nonsmooth problem in l1 norm,this paper proposes a new Maximum Entropy Function Method （MEFM） to solve the l1 optimization problem via smoothing the objective function with maximum entropy function.Intimately relating to homotopy method,MEFM provides a systematic approach for deriving the global optimal sparse solution.Finally,the numerical results show that it is an effective technique for signal reconstruction.In a CS framework,MEFM is a usefully alternating method to solve the l1 optimization problem.

关 键 词：压缩感知 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]