基于迭代迭差与延拓算法的MP稀疏分解研究  

MP sparse decomposition based on iterative residual and extension algorithm

作　　者：李振 李伟光[1] 赵学智[1] 林鑫 LI Zhen;LI Weiguang;ZHAO Xuezhi;LIN xin(School of Mechanical and Automotive Engineering,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学机械与汽车工程学院,广州510640

出　　处：《振动与冲击》2018年第17期161-168,177,共9页Journal of Vibration and Shock

基　　金：国家高计划研究发展计划(863计划)(2015AA043005)

摘　　要：匹配追踪算法(Matching Pursuit,MP)常用于实现信号的稀疏分解,经典的MP分解算法挑选最佳核函数的判定准则是原函数在该核函数上的投影最大,这种判定准则往往会造成重构后的信号误差增大,针对这一问题提出了迭代迭差算法,实例表明该准则比经典MP算法的重构误差小。同时,发现经典MP算法或迭代迭差算法在进行信号稀疏分解时会产生端点效应,使得重构信号在端点处存在较大误差,为解决该问题提出了一种基于多项式拟合的延拓算法,比较理想地解决了信号稀疏分解产生的端点效应,实例结果表明此算法比单纯的增加迭代次数来减弱端点效应更有效。The matching pursuit(MP)algorithm is usually used to realize signals’sparse decomposition.In the classical MP algorithm,the criterion for selecting the optimal core function is that the primitive function and the core function have the largest inner product.However,this criterion may cause reconstructed signals to have large error.Aiming at this problem,the iterative residual criterion was proposed.Many examples showed that this criterion causes reconstructed signals to have a smaller error.Meanwhile,the endpoint effect was detected in both the classical MP algorithm and the iterative residual algorithm to cause reconstructed signals having a larger error at an endpoint.In order to solve this problem,an extension algorithm based on polynomial fitting was proposed.Example results showed that this algorithm is more effective than the iterative residual algorithm be to weaken the endpoint effect.

关 键 词：稀疏分解 迭代迭差判定准则 端点效应 延拓方法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] TK267[自动化与计算机技术—控制科学与工程]