基于静态小波变换的提升框架分解

静态小波变换的最大优点是具有平移不变性。该文基于小波变换的多相表示,利用多采样率滤波器理论中上(下)采样算子与滤波器的等效易位关系,提出了将传统的静态小波变换由懒惰小波变换经过有限步交替的提升和对偶提升结构来实现的方法。由于提升框架容易实现逆变换,故在处理边界中具有更大的灵活性。分析表明,与标准算法相比,通过提升分解,可减少一半计算量。

Lifting Factorization Based on Stationary Wavelet Transform

The main advantage of the stationary wavelet transform is the translation invariance of the wavelet coeffi-cients.In this paper,based on the polyphase representation of wavelet transform,a new structure is proposed to that the traditional stationary wavelet transform can be obtained with a finite number of lifting steps and dual lifting steps start-ing from the Lazy wavelet,using the equivalent relation of position-swapping between up(down)sampler and filter in the multi-rate filter banks.Because of this easy inversion,the new structure offers a great flexibility in treating boundary conditions.Furthermore,we present that the cost of lifting factorization is one half of the cost of the standard algorithm.