基于时间分数阶非线性扩散模型的平滑方法

Smoothing method based on time-fractional nonlinear diffusion model

针对信号降噪问题,结合经典非线性扩散滤波和分数阶导数,提出了一种时间分数阶非线性扩散的平滑方法,该方法是在经典非线性扩散模型的基础上将时间导数改为分数阶导数得到的。首先,给出了时间分数阶扩散滤波的数值算法;然后,与经典平滑方法(非线性扩散滤波、正则化方法、Savitzky-Golay法和小波法)进行了比较。结果表明,时间分数阶扩散模型在信噪比和均方根误差方面均有更大的改善;与经典平滑方法相比较,所提方法明显具有更优越的性能。

For the problem of signal denoising,this paper proposed a time-fractional nonlinear diffusion smoothing method by combining the classical nonlinear diffusion filtering and the fractional derivative.The proposed model used the fractional order time derivative to replace the time derivative in the classical nonlinear diffusion model.Firstly,it developed the numerical algorithm for the time-fractional nonlinear diffusion filtering,and then compared the proposed method with the classical smoo-thing methods(nonlinear diffusion filtering,regularization method,Savitzky-Golay method and wavelet method).The result shows that the time-fractional diffusion filtering method has a greater improvement in signal-to-noise ratio and root mean square error.Compared with the classical smoothing method,the proposed model obviously has a more excellent performance.