离散小波变换的最优Lifting分解方法

现有Lifting分解(Lifting Factorization,LF)算法不能在较短时间内求解出较长离散小波变换(Discrete Wavelet Transform,DWT)滤波器组的所有数值稳定LF,更无法计算最优LF.在LF的形式化分析基础上,提出了DWT多相矩阵的常数最大公因子分解方法,极大缩小了分解搜索空间;进一步,从数值稳定性及计算复杂性两方面研究了LF评价问题;最后,提出了基于联合优化的最优LF算法.实验结果表明,本文算法在解的质量、求解时间及适用范围上都有较大改进.

An Approach to the Optimal Lifting Factorization of DWT

Lifting factorization (LF) was one of the latest advancements of study on fast DWT implementations.Because of exponential size of the factorization set,known algorithms could not find in reasonable time all stable (to say nothing of optimal) LFs of a given DWT with long filters.In this paper,a so-called constant GCD (Greatest Common Divisor) factorization approach to FIR polyphase matrix was given,which contracted considerably the factorization space.Furthermore,the problem of how to evaluate a certain LF was investigated in terms of both numerical stability and computation complexity.Consequently,an algorithm called OLFA (Optimal LF Algorithm) was readily available.All of the theoretical results were constructively proven.Experimental data show that OLFA obtains considerable improvements in solution quality,computation time and application range over the existing algorithms,thus makes LF a tool of great generality and practicability for fast DWT implementations.