Title :
Analyzing the Optimality of Predictive Transform Coding Using Graph-Based Models
Author :
Zhang, Cha ; Florêncio, Dinei
Author_Institution :
Microsoft Res., Redmond, WA, USA
Abstract :
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.
Keywords :
Gaussian processes; Markov processes; discrete cosine transforms; graph theory; image coding; transform coding; 2D DCT; 2D discrete cosine transform; 2D first-order GMRF; GMRF model; Gaussian Markov random field model; coding efficiency; graph transform; graph-based model; intraframe predictive coding; motion prediction; precision matrix eigenanalysis; predictive transform coding optimality; signal decorrelation; theoretical analysis; Analytical models; Correlation; Covariance matrix; Decorrelation; Discrete cosine transforms; Transform coding; Gaussian Markov random field; graph-based models; predictive coding; transform coding;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2012.2230165
