提升小波构造方法的改进

Improvement of Construction Method for Lifting Wavelet Transform

提出了提升小波的改进构造方法。当he(z)和ho(z)因式分解为奇数个多相矩阵相乘,但是ge(z)和go(z)因式分解成偶数个多相矩阵相乘时,从ge(z)和go(z)入手,实现首先进行预测的多步提升;以及当he(z)和ho(z)因式分解成奇数个多相矩阵相乘时,仍然从he(z)和ho(z)因式分解入手可以采用的新方法,为求取小波滤波器组的提升方案提出了更全面的解决方法。提升小波变换采用分裂、预测和更新三个过程的提升方案,应用范围更广,计算速度更快。

An improved method for constructing lifting wavelet is presented. When the number of polyphase matrix（ho（z） and ho（z） are decomposed） is odd, and the number of the polyphase matrix （ge（z） and go（z） are decomposed） is even, the factorization of ge（z）and go（z） is carried out. Moreover, if the number of the polyphase matrix （he（z） and ho（z） are decomposed） is odd, the factorization of ho（z） and ho（z） is carried out by using an improved method to realize the comprehensive lifting scheme. Finally, the lifting wavelet has characteritics of faster speed and broader range of application by dividing the transform process into three phases ： split, prediction and updating.