Suboptimality of the Karhunen-Loeve transform for transform coding

Abstract

The performance of the KLT for transform coding applications was examined. The KLT has long been viewed as the available block transform for transform coding. The fixed-rate and variable-rate transform codes were also presented. The fixed-rate approach uses an optimal fixed-rate scalar quantizer to describe the transform coefficients; the variable-rate approach uses a uniform scalar quantizer followed by an optimal entropy code. Earlier work shows that for the variable-rate case, there exist sources on which the KLT is not unique and the optimal transform code matched to a worst KLT yields performance as much as 1.5 dB worse than the optimal transform code matched to a best KLT. The results were strengthened to show that in both the fixed-rate and the variable-rate coding frameworks, there exist sources for which the performance penalty for using a worst KLT can be made arbitrarily large. Further demonstrations in both frameworks show that there exist sources for which even a KLT gives suboptimal performance. Finally, the results show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding.