基于奇异值的小波变换微弱信号消噪法

De-Noising Method for Weak Signal of Wavelet Transformation Based on Singular Value

针对信噪比低、噪声非均匀分布的弱信号消噪效果不佳的问题，提出一种基于有效奇异值分解和小波阈值消噪相结合的方法。通过构造相空间矩阵并对其进行奇异值分解（singular value decomposition，SVD），得到一系列正交子空间；根据信号和噪声对奇异值贡献不同，通过奇异值最小二乘误差判定法进行有效奇异值选择，并利用子空间重构信号。仿真实验表明：本方法提取出的信号完整性更好，信噪比更高。

In view of the deficiencies with low signal noise ratio （SNR） and non-uniform noise distribution, an algorithm based on singular value decomposition （SVD） plus wavelet threshold de-noising is presented. The phase space matrix is constructed by SVD, getting a series of orthogonal subspaces. According to the different contribution of signal and noise for the singular value, a determine method about the least squares error is proposed for estimating the number of effective singular value. The subspaces reconstruct signal by the wavelet threshold method. The results show that the extracted signals have better integrity and higher SNR.