改进的双小波空域相关混沌信号降噪方法

Improved Dual-Wavelet Spatial Correlation Method for Denoising of Chaotic Signals

基于小波系数尺度间的相关性原理,提出一种改进的基于双小波的空域相关混沌信号降噪方法。首先将单个离散小波变换扩展为两个,然后对每个小波变换后的近似系数进行奇异谱分析,对细节系数进行尺度间的相关性分析,最后将处理后的近似部分和细节部分分别取平均再重构得到降噪后的信号;同时还引入了一个判别系数,对相关量进行自适应的选取。通过对Lorenz模型和月太阳黑子混沌信号进行仿真分析,证实了所提方法具有实现简单、重构误差小的优点,能够对实际观测混沌信号进行有效的降噪。

Based on the theory of wavelet coefficients correlation between scales, an improved dual-wavelet spatial correlation method was proposed for denoising of chaotic signals. First, the DWT was extended from using one wavelet to using two, then the approximate coefficients after every DWT were handled by the singular spectrum analysis （SSA） and the detail coefficients were analyzed by the correlation theory between scales, finally the signal was reconstruction after seeking the average of the approximate and the detail parts respectively; At the same time, a discriminant factor was introduced in order to choose the correlation volume adaptively. The chaotic signals generated by Lorenz model and sunspots were respectively applied for simulation analysis. The numerical experiment results confirm the advantages of the method including the simple of realizing, the small reconstruction error, and the effective of denoising in chaotic signals observed.