Analyzing the Optimality of Predictive Transform Coding Using Graph-Based Models

In this letter, we provide a theoretical analysis of optimal predictive transform coding based on the Gaussian Markov random field (GMRF) model. It is shown that the eigen-analysis of the precision matrix of the GMRF model is optimal in decorrelating the signal. The resulting graph transform degenerates to the well-known 2-D discrete cosine transform (DCT) for a particular 2-D first order GMRF, although it is not a unique optimal solution. Furthermore, we present an optimal scheme to perform predictive transform coding based on conditional probabilities of a GMRF model. Such an analysis can be applied to both motion prediction and intra-frame predictive coding, and may lead to improvements in coding efficiency in the future.