基于迭代迭差与延拓算法的MP稀疏分解研究

李振,李伟光,赵学智,林鑫

振动与冲击 ›› 2018, Vol. 37 ›› Issue (17) : 161-168.

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PDF(3517 KB)
振动与冲击 ›› 2018, Vol. 37 ›› Issue (17) : 161-168.
论文

基于迭代迭差与延拓算法的MP稀疏分解研究

  • 李振,李伟光,赵学智,林鑫
作者信息 +

MP sparse decomposition based on iterative residual and extension algorithm#br#

  • LI Zhen,LI Weiguang,ZHAO Xuezhi,LIN xin
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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较大,针对这一问题本文提出了迭代迭差算法,实例表明该准则比经典MP算法的重构信号误差小。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要有效。

Abstract

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

Key words

sparse decomposition / iterative residual criterion / endpoint effect / extension algorithm

引用本文

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李振,李伟光,赵学智,林鑫. 基于迭代迭差与延拓算法的MP稀疏分解研究[J]. 振动与冲击, 2018, 37(17): 161-168
LI Zhen,LI Weiguang,ZHAO Xuezhi,LIN xin. MP sparse decomposition based on iterative residual and extension algorithm#br#[J]. Journal of Vibration and Shock, 2018, 37(17): 161-168

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