引入参考信号的新峭度快速不动点算法  

Fast Fixed-point Algorithm for New Kurtosis by Introducing the Reference Signals

作　　者：赵伟[1] 沈越泓[1] 项海涛[2] 袁志刚[1] 徐鹏程[1] 魏以民[1] 简伟[1] 

机构地区：[1]解放军理工大学通信工程学院,南京210007 [2]国防信息学院,武汉430010

出　　处：《信号处理》2014年第12期1486-1495,共10页Journal of Signal Processing

基　　金：国家自然科学基金资助项目(61172061);江苏省自然科学基金资助项目(BK2011117)

摘　　要：在盲源分离和独立成分分析中,峭度是衡量随机信号非高斯性的常用对比准则,通过不同类型的算法对其进行优化,找到非高斯性极大值点,即实现了源信号的提取或分离。例如,基于峭度的快速不动点算法,它是一种收敛速度很快的算法。最近,Marc Castella等人提出了一类基于所谓"参考信号"的对比准则,以及对应的梯度最大化优化算法,这些算法具有很好的收敛性能。受其启发,文章以一种类似的方式将"参考信号"思想应用到峭度中,得到一种新颖的对比函数,并基于该新峭度对比函数,提出了一种新的快速不动点算法。与经典的基于峭度的快速不动点算法相比,该算法极大地提高了收敛速度,尤其是随着信号样值点数的增加,该算法的优势会更加明显。文章分析和证明了该新峭度对比函数的局部收敛性,给出了新算法的详细推导过程,仿真实验验证了该算法的性能,并与经典算法进行了比较分析。In the blind source separation （BSS）and independent component analysis （ICA）,kurtosis is a common contrast measure for non-gaussianity of stochastic signals.The source signals can be extracted or recovered by using different optimization algorithms to find the non-gaussianity maximization points.For instance,the fast fixed-point algorithm based on kurtosis is a very classical one,which has very fast convergence speed.Recently,a family of so-called reference-based contrast criteria have been proposed by Marc Castella etc,and corresponding gradient maximization algorithms have also been proposed,which show very good performance.Inspired by them,the reference-based scheme is applied in kurtosis to construct a new kurtosis contrast function in a similar manner,based on which a novel fast fixed-point algorithm is proposed in this paper.Compared with the classical kurtosis-based fast fixed-point algorithm,this new algorithm is much more efficient in terms of computational speed,which is significantly apparent with large number of samples.The local consistency of this new contrast function is an-alyzed and proved,and the derivation of this new algorithm is also presented in detail.The performance of this new algorithm is validated through simulations,together with corresponding comparison and analysis.

关 键 词：盲源分离 独立成分分析 峭度 快速不动点算法 对比函数 参考信号 

分 类 号：TN911.23[电子电信—通信与信息系统]