任意阶PDE降噪特性分析

通过对分数阶微积分原理的研究,提出了任意阶偏微分方程(partial differential equations,简称PDE)降噪的统一模型,实现了基于任意阶PDE降噪的数值化方法,并分析了任意阶PDE降噪特性。该数值化方法能够快速实现信号降噪,耗时少。通过仿真实验,分析了PDE降噪性能的影响因素,与其他去噪方法进行了对比分析,并对现场实测信号进行了降噪分析。结果表明,PDE数值求解降噪方法性能优良,算法简单。

Noise Reduction Features of Arbitrary Order Partial Differential Equations

According to the principle of fractional calculus, a unified model of arbitrary order partial differential equation (PDE) based noise reduction was proposed. The design method based on the numerical solution for arbitrary order PDE filter was realized. In particular, the filter features of arbitrary order PDE were analyzed. The numerical procedure has rapid implementation of the filtering procedure with one iteration, which has good time-consuming performance. De-noising tests were conducted on different degrees of artificial noise. Experimental tests have been rigorously compared with different de-noising methods to verify the efficacy of the proposed method. It turns out that the numerical process to PDE noise reduction has an excellent performance and a simple algorithm.