New method for 2D nonlinear lifting wavelet transform

Nonlinear multiresolution signal decomposition schemes is a new tool developed over the past years. The lifting scheme introduced by Sweldens also provides a useful way to construct nonlinear wavelet decompositions freely. In this paper, based on a certain statistical operator defined here, a new method of nonlinear' wavelet decomposition is proposed, which is suited for the task of image compression, especially for lossless coding applications. It can be used to realize the integer-valued wavelet transform, which can avoid quantization with the image detail signals being zero (or almost zero) at the smooth gray level variation areas at big probability. Numerical results show that the entropy of the coefficients in the transform domain obtained with this new method is smaller than that obtained with other nonlinear transform methods.