Image compression via joint statistical characterization in the wavelet domain

We develop a probability model for natural images, based on empirical obser vation of their statistics in the wavelet transform domain. Pairs of wavele t coefficients, corresponding to basis functions at adjacent spatial locati ons, orientations, and scales, are found to be non-Gaussian in both their m arginal and joint statistical properties. Specifically, their marginals are heavy-tailed, and although they are typically decorrelated, their magnitud es are highly correlated. We propose a Markov model that explains these dep endencies using a linear predictor for magnitude coupled with both multipli cative and additive uncertainties, and show that it accounts for the statis tics of a wide variety of images including photographic images, graphical i mages, and medical images. In order to directly demonstrate the power of th e model, we construct an image coder called EPWIC (embedded predictive wave let image coder), ih which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional pr obabilities calculated from the model. Bitplanes are ordered using a greedy algorithm that considers the MSE reduction per encoded bit. The decoder us es the statistical model to predict coefficient values based on the bits it has received. Despite the simplicity of the model, the rate-distortion per formance of the coder is roughly comparable to the best image coders in the literature.