Suboptimality of the Karhunen-Loève transform for transform coding

Abstract

We examine the performance of the KLT for transform coding applications. The KLT has long been viewed as the best available block transform for transform coding. This paper treats fixed-rate and variable-rate transform codes. The fixed-rate approach uses an optimal fixed-rate 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. In this paper, we strengthen that result to show that in both the fixed-rate and the variable-rate coding frameworks there exist sources for which the performance penalty for a "worst" KLT can be made arbitrarily large. Further, we demonstrate in both frameworks that there exist sources for which even a best KLT gives suboptimal performance. Finally, we show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding.

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