小波阈值去噪函数的改进方法分析

Analysis of Modified Methods of Wavelet Threshold De-noising Functions

小波阈值去噪是一种简洁有效的去噪方法,传统阈值去噪法包括软、硬阈值法,它们在实际应用中取得了很大的成功,但同时也存在一些有待改进的地方。为此,介绍了3种国内外有代表性的小波阈值函数改进方法,并在传统阈值函数的基础上提出了一种新的双变量阈值函数。对局部放电仿真信号进行的去噪分析结果显示,改进阈值函数在信噪比增益和最小均方误差意义上要优于传统的软、硬阈值函数,其中新的双变量阈值函数在4种改进阈值函数中具有最优的去噪性能。

Threshold de-noising, one of the wavelet de-noising methods, is an effective tool in signal processing. The traditional threshold de-noising functions are soft and hard threshold functions, and they were used successfully in practical application, however, there are also some places that need to be improved. In this paper, three modified methods which were proposed both at home and abroad were introduced, and a new threshold de-noising function with double variable parameters is proposed, and it can give different de-noising results only by changing the values of variable parameters. Compared with the soft and hard threshold functions, this new threshold function has one- order continuous derivatives, and there is a smooth transition region between noise and signal, according to the continuous characteristic of the natural signal. Meanwhile, soft and hard and those four modified threshold functions are used in partial discharge signal de-noising. The simulation experiment results of signal de-noising indicate that those modified methods give better MSE performance and SNR gains than the soft and hard threshold functions do. In those six threshold functions, the new proposed double-variable threshold function has the best de-noising results only by changing the variable parameters, and it is more elastic than the traditional threshold functions. This new threshold function makes it possible to construct an adaptive wavelet threshold de-noising algorithm, offers a new choice for wavelet threshold de-noising, and makes it possible to embody the advantages of the wavelet threshold denoising method more fully.