On the efficient memory usage in the lifting scheme for the two-dimensional wavelet transform computation

In this paper, a new algorithm to efficiently implement the two-dimensional lifting scheme is presented. The 1D lifting-scheme performs in-place processing of the input samples, and hence it provides reduction in memory requirements. However, for image processing (2D), in-place computation is not enough, resulting in a memory-intensive algorithm, since it has to keep the whole image in memory. We propose the use of line-by-line processing algorithm for the lifting scheme, and we address some issues on how to perform synchronization among different buffer levels, so that an implementation can be easily written. Experimental results show that, for a 5-megapixel image, our algorithm requires 200 times less memory and it is more than 3 times faster than the usual one.