From Mixtures of Mixtures to Adaptive Transform Coding

Abstract

We establish a principled framework for adaptive transform cod(cid:173) ing. Transform coders are often constructed by concatenating an ad hoc choice of transform with suboptimal bit allocation and quan(cid:173) tizer design. Instead, we start from a probabilistic latent variable model in the form of a mixture of constrained Gaussian mixtures. From this model we derive a transform coding algorithm, which is a constrained version of the generalized Lloyd algorithm for vector quantizer design. A byproduct of our derivation is the introduc(cid:173) tion of a new transform basis, which unlike other transforms (PCA, DCT, etc.) is explicitly optimized for coding. Image compression experiments show adaptive transform coders designed with our al(cid:173) gorithm improve compressed image signal-to-noise ratio up to 3 dB compared to global transform coding and 0.5 to 2 dB compared to other adaptive transform coders.