多尺度B样条小波变换去除噪声的一种方法

A Method of Denoising by Multl-scale B SPline Wavelet Transform

基于Ｂ样条小波的特点，利用小波变换引出了Ｂ样条小波实现信号分解和重构的实用公式．从理论和实验两个角度分析了不同噪声在小波变换下的传播性：白噪声和尖脉冲由于具有负奇异性和稠密性及方差均随尺度的增大而减少，据此提出一种用小波变换去除随机噪声的新算法．经过实验，与过去常用的均值滤波和中值滤波方法进行对比认为，该方法对白噪声和尖脉冲噪声均有良好的抑制作用，对信号的突变信息和波形都有较好的恢复作用，克服了均值滤波及中值滤波法造成原信号边缘模糊的缺陷．该方法可推广到其它信号的处理，具有一定的理论意义和实用价值．

Based on the characteristics of B spline wavelet,the practical formulae are derived for decomposition and reconstruction of signals by wavelet transform. The propagation behavior of the wavelet transfom of white noise and spike pulse,negative singularity and the average density of modulas of maxima and variance decreasing with increasing of scale,are analysed in theory and with experiment. According to the propagation behavior,a new method is put forward for removing random noise from signals by wavelet transform. The method has better attenuation to the noises and better restoration to sudden changes of waveform of a signal than mean filter and midvalue filter. It overcomes the shortcoming of obscure border of original signal caused by mean filter and midvalue filter. It can also be used for processing of other signals and has practical value.