多级多维离散小波变换的快速提升计算

Fast Lifting Algorithm for Multi-Level and Multidimensional Discrete Wavelet Transform

提升方法是计算离散小波变换的有效手段 ,它由一系列的提升步和拉伸变换组成 .在计算多级和多维离散小波变换时 ,现有方法在每一次小波分解的过程中都做完整的提升步计算和拉伸变换计算 .我们发现该方法存在运算过程的冗余 ,为此本文提出了一种称之为后拉伸变换的提升方法 ,基本思想是计算完所有的提升步后 ,再统一进行拉伸变换 .它能减少离散小波变换的乘法运算量 .例如 ,对图像与视频压缩中应用广泛的Daubechies 9/7小波 ,做一维 5级分解时与现有方法相比 ,乘法运算减少 2 0 %,而二维 5级分解时 ,乘法运算减少 2 8%.

Lifting Scheme can be used to calculate Discrete Wavelet Transform (DWT) efficiently. It is composed of a number of lifting steps and the scaling transform. When it is used to calculate multi-level and multidimensional DWT, there exist many redundant multiplications. We propose, a new technique, called Post-Scaling Lifting Algorithm (PSLift), which needs fewer multiplications. The basic idea is first to calculate all lifting steps of each level and each dimensional DWT, and then calculate the scaling transform. For example, when five level decompositions are implemented for Daubechies 9/7 biorthogonal wavelet, compared to the known methods, the number of multiplication needed is reduced by 20% and 28% for one dimensional DWT and two dimensional DWT.