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

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2 Author(s)
Cha Zhang ; Microsoft Res., Redmond, WA, USA ; Florencio, D.

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.

Published in:

Signal Processing Letters, IEEE  (Volume:20 ,  Issue: 1 )