小波滤波中的阈值研究

Thresholds in wavelet filtering

小波阈值滤波是利用小波变换,除去小幅度的小波系数,收缩或保留幅度较大的小波系数,抑制信号中的噪声。实验证明,利用半软阈值滤波,若下阈值取得过小,不利除噪,取得过大,又不利保留信号中的细节;若上阈值取得过大,将产生较大的偏差,取得过小,又将产生较大的方差。滤波阈值的确定是小波阈值滤波的关键问题,直接决定着滤波效果。对小波阈值滤波的上、下阈值选取进行了深入研究,通过实验总结,建立了求解最优上、下阈值的目标函数,利用扫描计算,得出了最优上、下阈值与噪声均方差之间的关系,上阈值系数约为4.3,下阈值系数约为3.7。并进行了仿真验证,滤波效果明显。

Wavelet threshold filtering is to remove smaller wavelet coefficients and shrink or keep larger wavelet coefficients by wavelet transform for the restraint of noises in signals. Experiments prove that,in semisoft threshold filtering,smaller bottom threshold is unfavorable to noise restraint while bigger one is unfavorable to signal detail reservation;bigger top threshold causes larger deviation while smaller one causes larger square deviation. The filtering effectiveness depends directly on the threshold setting. The way to determine the bottom and top thresholds is studied and the objective function of optimal bottom and top thresholds is established based on experiments. The relationship between threshold and noise mean square deviation is achieved by scanning calculation. The top threshold coefficient is about 4.3 and the bottom threshold coefficient is about 3.7. Simulation demonstrates the obvious filtering efficiency.