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.