Fast lifting wavelet transform and its implementation in Java

摘要

Fast lifting wavelet transform is a technique which replaces standard discrete wavelet transform used in computation of wavelet coefficients. The idea of lifting comes from the lifting scheme, a method used in wavelet design. The standard method relies on convolution of the original signal with FIR filter structures. Fast lifting scheme basically breaks up the original filters into a series of smaller structures, providing a very sophisticated and versatile algorithm that is up to 50percent faster than the standard way with no extra memory requirements. This paper discusses an implementation of this algorithm in Java language, comparing both speed and efficiency of standard and fast lifting wavelet transform for CDF 9/7 filters, which are used in lossy image compression in JPEG2000 standard. Java has been chosen for its platform independent character and easy integration in mobile devices.