Suboptimality of the Karhunen-Loeve transform for transform coding
Michelle Effros, Hanying Feng, K. Zeger · 2003
The performance of the KLT for transform coding applications was examined. The KLT has long been viewed as the best 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 best 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.