Abstract: According to the different characteristics of signals and Gaussian noises, a noise reduction method is proposed based on local projection and lifting wavelet for chaotic signals. Lifting wavelet transform is used to obtain the approximate coefficient, and the phase space of which is reconstructed. It is compared to the phase space of the observed chaotic signals in order to select the local neighborhood of the local projection. Singular Spectrum Analysis（SSA） is combined in the local neighborhood, which uses the main components representing the attractors to reconstruct the chaotic signals. The chaotic time series generated by Lorenz model and monthly sunspot are respectively applied for simulation analysis. The numerical experiment results confirm the effect of the method raised for noise reduction of the observed chaotic signals.

Key words: chaotic signals, local projection, lifting wavelet, Singular Spectrum Analysis（SSA）, noise reduction

摘要： 根据信号和噪声的不同特性，提出了一种基于局部投影和提升小波的混沌信号降噪方法。该方法利用提升小波变换得到实际混沌信号的近似系数，对其进行相空间重构，与实际混沌信号的重构相空间进行比较，来选取局部投影的邻域，在局部邻域内进行奇异谱分析，利用代表吸引子的主分量来重构混沌信号。通过对Lorenz模型和月太阳黑子进行仿真分析，证实了提出方法对混沌信号降噪的有效性。

关键词: 混沌信号, 局部投影, 提升小波, 奇异谱分析, 降噪