基于提升格式的M带自适应小波变换

M-Band Adaptive Wavelet Transform Based on Lifting Scheme

提出了基于提升格式的M带自适应小波设计方法。首先设定M带提升小波预测算子与更新算子的基本形式,然后根据提升结构及所选取的误差准则来自适应地调整预测算子及更新算子的系数,从而得到适合给定应用的最优M带提升小波。与目前对M带小波的研究相比较,采用提升格式得到的M带自适应小波既保持了提升方法的快速、简单及可直接在时(空)域上运算的特点,又具有根据实际问题设计出优化小波的优势。给出了两个3带自适应提升小波的设计实例。

M-band adaptive wavelet design based on the lifting scheme is proposed. Firstly, the basic structures of predictor and update operator are set according to specific application. Based on lifting structure and error criteria, coefficients of predictor and update operator are tuned to find the exact wavelet adapted best to the given application of the wavelet transform. Compared with current researches on M-band wavelet, the design method holds all the merits from lifting scheme, such as fast speed, calculation simplicity and construction in spatial domain. It has advantages of designing optimal wavelet according to real needs. Finally, two three-band adaptive wavelet design examples by a lifting scheme are given based on the method.