摘要
针对奇异值分解信号降噪方法中吸引子轨迹矩阵(Hankel矩阵)结构的确定,以及有效奇异值的选择两个关键问题,提出了一种基于遗传算法的奇异值分解信号去噪算法。首先,利用原始信号构造Hankel矩阵,运用遗传算法对矩阵结构进行优化,然后对含噪声信息的矩阵进行奇异值分解,最后通过K-medoids聚类算法确定有效奇异值个数,对有效奇异值和其对应的向量进行奇异值分解反变换,还原原始信号,达到去噪目的。通过仿真实验并与小波包变换、小波变换以及传统快速傅氏变换(FFT)去噪方法相比较,结果表明该算法具有良好的去噪效果。
For singular value decomposition signal de-noising algorithm, the method of confirming the structure of attractor trajectory matrix （Hankel matrix） and the way to ascertain effective singular values both are key problems. In order to solve these two problems, this paper proposed a singular value decomposition signal de-noising algorithm based on genetic algorithm. Firstly, this algorithm constructed a Hankel matrix with the original signal, and utihzed GA to optimize the matrix structure. Then it conducted singular value decomposition transformation on the matrix. Finally, it worked out the number of useful singnlar values by K-medoids clustering algorithm, and reconstructed the signal with the method of conducting inverse singular value decomposition transformation on the values and their corresponding vectors to achieve the purpose of signal de-noising. Through simulation experiments, comparing the in this paper proposed algorithm with wavelet packet transform, wavelet transform and traditional fast Fourier transformation （FFT） signal de-noising algorithm, it shows that the algorithm here has a positive effect on signal de-noising.
出处
《计算机应用研究》
CSCD
北大核心
2015年第8期2281-2285,共5页
Application Research of Computers
基金
河北省自然科学基金资助项目(F2014502050)
中央高校基本科研业务费专项资金资助项目(2014MS127)
关键词
遗传算法
奇异值分解
K-medoids聚类算法
有效奇异值
信号去噪
genetic algorithm
singular value decomposition
K-medoids clustering algorithm
effective singular values
signal de-noising
