基于小波包变换的自适应混沌信号降噪算法

Adaptive Noise Reduction Algorithm for Chaotic Signals Based on Wavelet Packet Transform

为了更好地体现混沌系统的内在特征,该文提出一种基于小波包变换的自适应混沌信号降噪算法。首先,该算法根据不同分解尺度小波包系数的相关性不同,确定了最佳分解层数;以对数能量熵为代价函数,得到了最优小波包基。然后,在局部邻域内对近似系数进行投影分析,利用神经网络梯度下降法对细节系数进行自适应选择。通过最小化损失函数,最大限度降低噪声对混沌信号的影响。最后,通过对来自Rossler混沌模型的状态变量进行仿真分析,证实了该算法对混沌信号降噪的优越性。

To reflect better the inherent characteristics of chaotic systems,an adaptive noise reduction algorithm for chaotic signals based on wavelet packet transform is proposed.Firstly,the best decomposition level is determined according to the different correlation of wavelet packet coefficients in different decomposition scales,while the optimal wavelet packet basis is obtained with the logarithmic energy entropy as the cost function.Then,the approximate coefficients are projected in the local neighborhood and the detail coefficients are adaptively selected with the gradient descent algorithm in neural network.By minimizing the loss function,the influence of noises on chaotic signals is reduced to the greatest extent.Finally,simulations on the state variables originating from Rossler chaotic model verify the denoising superiority of the proposed algorithm for the chaotic signals.