A jointly optimized subband coder

Rate-distortion-constrained subband video coding

This paper introduces a subband video coding algorithm for operation over a continuum of rates from very low to very high. The key elements of the system are statistical rate-distortion-constrained motion estimation and compensation, multistage residual quantization, high order statistical modeling, and arithmetic coding. The method is unique in that it provides an improved mechanism for dynamic spatial and temporal coding. Motion vectors are determined in a nontraditional way, using a rate-distortion cost criterion. This results in a smoother and more consistent motion field, relative to that produced by conventional block matching algorithms. Control over the system computational complexity and performance may be exercised easily.

Image compression via joint statistical characterization in the wavelet domain

We develop a probability model for natural images, based on empirical observation of their statistics in the wavelet transform domain. Pairs of wavelet coefficients, corresponding to basis functions at adjacent spatial locations, orientations, and scales, are found to be non-Gaussian in both their marginal and joint statistical properties. Specifically, their marginals are heavy-tailed, and although they are typically decorrelated, their magnitudes are highly correlated. We propose a Markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties, and show that it accounts for the statistics of a wide variety of images including photographic images, graphical images, and medical images. In order to directly demonstrate the power of the model, we construct an image coder called EPWIC (embedded predictive wavelet image coder), in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model. Bitplanes are ordered using a greedy algorithm that considers the MSE reduction per encoded bit. The decoder uses the statistical model to predict coefficient values based on the bits it has received. Despite the simplicity of the model, the rate-distortion performance of the coder is roughly comparable to the best image coders in the literature.