一种基于SVD分解的小波阈值降噪方法

Wavelet Threshold Denosing Based on Singular Value Decomposition

针对小波软阈值消噪的缺点,探讨了一种基于奇异值分解(SVD)的离散小波去噪方法。该方法通过对每层小波分解细节系数进行奇异值分解,将其中的信号特征成分和噪声分解到不同的正交子空间中,在子空间中选取集成信号特征成分的奇异值矢量进行重构,从而提取出淹没在细节系数中的有用信号成分,最后进行小波重建,得到降噪信号。通过仿真实例的验证,表明该方法与小波阈值消噪法相比,在强噪声背景下,它提取出的信号特征成分更完整,信噪比更高。

Aiming at the deficiency of wavelet soft-thresholding denoising, a new wavelet transform denoising method based on sin- gular value decomposition （SVD） was proposed. The detailed coefficients of DWT contain signal and noise. Instead of the soft-thresh- olding method, SVD is applied to decompose the signal features and noise into different orthogonal subspaces. With the reconstruction of the singular vectors in subspace, the signal features are extracted effectively. Experimental results show that the approach, compared with the soft-thresholding denoising, is an efficient tool to extract useful component from high-noise signals.