基于提升的自适应非线性小波变换研究

Adaptive Nonlinear Wavelet Transform Based on Lifting Schemes

针对传统小波变换在处理信号时缺乏自适应能力的缺点,提出一种新的自适应小波变换算法。该算法主要基于信号的局部结构特征的相关性,及这种相关性所表现出的方向性,利用这些信息采用自适应提升策略来构造小波。给出了一种新的自适应非线性更新算子U的结构,并证明了采用此结构分解的小波可很方便地实现完全重构。先给出算法结构的一般框架,然后给出了在一维和二维情况下具体实现的例子。试验表明该算法优于一般算法,和其它自适应小波算法相比,本算法有更强的自适应能力和更大的灵活性。

To overcome the shortcoming that the classical wavelets transform lack of the adaptive capacity in signal process, a novel adaptive wavelet transform scheme was proposed, which is mainly based on the correlation of local structure of the signal and the direction with which the correlation was characterized. This information could be utilized to construct adaptive wavelets decompositions via lifting scheme. A new adaptive nonlinear update operator U was proposed, and it was proved that the wavelets, which were decomposed by this kind of structure, could realize conveniently the perfect reconstruction without any overhead cost. A general framework of the new algorithm is put forward, and then the specific examples in 1-D and 2-D case were shown. The tests demonstrate that the new one is better than the Iraditional schemes, and has great flexibility and fine potential for expansion than other adaptive methods.