Suboptimality of the Karhunen–LoÈve Transform for Transform Coding

Suboptimality of the Karhunen-Loeve transform for fixed-rate transform coding

AbstractAn open problem in source coding theory has been whether the Karhunen-Loève transform (KLT) is optimal for a system that orthogonally transforms a vector source, scalar quantizes the components of the transformed vector using optimal bit allocation, and then inverse transforms the vector. Huang and Schultheiss proved in 1963 that for a Gaussian source the KLT is mean squared optimal in ...

On the Suboptimality of Orthogonal Transforms for Single- or Multi-Stage Lossless Transform Coding

Orthogonal transforms are compared with the causal transform in lossless transform coders. For single-stage lossless coding, it was shown in [1] that the integer-to-integer implementation of the best orthogonal decorrelating transform, the KLT, leads to lower compression performance than its causal counterpart. In this work, we pursue this analysis in the framework of a multi-stage lossless cod...

The Coding-Optimal Transform

We propose a new transform coding algorithm that integrates all optimiza tion steps into a coherent and consistent framework Each iteration of the algorithm is designed to minimize coding distortion as a function of both the transform and quantizer designs Our algorithm is a constrained version of the LBG algorithm for vector quantizer design The reproduction vectors are constrained to lie at t...

Transform Coding of Images

Beyond Traditional Transform Coding

Beyond Traditional Transform Coding