A two-dimensional lifting scheme of integer wavelet transform for lossless image compression

For the separable two-dimensional wavelet transform, its 2D lifting scheme is implemented by a sequence of one-dimensional wavelet transforms, and the corresponding 2D integer version is built in a similar way. In this paper, by introducing and investigating a matrix representation of the separable two-dimensional wavelet transform, we propose a new 2D lifting scheme and its integer version, where the lifting steps operate on the image directly. It is proved that they have less multiplication number than the classical ones, and the 2D integer wavelet transform is different from the classical 2D integer wavelet transform. Experiments indicate that, for the popular (5-3) filter, the 2D integer wavelet transform can achieves a little better compression than the classical one. The paper also compares JPEG2000 with JPEG-LS by experiments on DEM lossless image compression.