The construction of a statistical prediction lifting operator and its application

A new method of nonseparable nonlinear wavelet decomposition is proposed, which is suited for the task of image compression, especially for lossless coding applications. It is based on a certain statistical operator that is defined here according to the Markov random field theory. In contrast to the previous nonlinear predictors such as the median or morphological operators, this statistical operator can sufficiently take advantage of the statistical correlation between neighboring pixels. It can be used to realize integer-valued wavelet transforms, which can avoid quantization with the image detail signals being zero (or almost zero) in the smooth gray-level variation areas at a 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 the other nonlinear transform methods.