自适应小波变换更新滤波器的优化研究

Study on optimal update filter based on lifting schemeadaptive wavelet transform

基于提升格式的小波变换被称为第二代小波变换,该种结构提供了一种灵活构造非线性小波分解和重构的方法。G.Piella根据提升格式小波变换的结构特点,提出了一种不需要额外附加信息就可完成精确重构的自适应更新滤波器,但算法只说明了滤波器系数需要满足精确重构的条件,没有具体说明如何确定滤波器的系数。在先选定预测滤波器的基础上,本文根据最小均方误差准则,提出了优化的小波更新滤波器的设计方法。最后以M IT/B IH数据库中心电图信号为例,通过与其他不同结构的小波变换进行比较分析,验证了优化的小波更新滤波器的性能。

Wavelet transforms via lifting scheme provides a general and an adaptive flexible tool for the construction of wavelet decompositions and perfect reconstruction filter banks.According to the construction of the lifting wavelet transforms,G.Piella presents an adaptive update lifting scheme,where the perfect reconstruction is possible without sending any side information.The perfect reconstruction condition for the filter coefficients is presented in G.Piella＇s algorithm,but the method for determining the filter coefficients is not illustrated.An optimal filter design method for the adaptive update wavelet transform is proposed.The optimal filter coefficients can be acquired based on the Minimum Mean Square Error Criteria（MMSE） in the algorithm.Compare with other wavelet transform filter,simulation results show that the optimal wavelet update filter presented by this paper can achieve the better linear approximation for the ECG data obtained from the M IT/B IH database.