Suboptimality of the Karhuenen-Loève Transform for Transform Coding

  • Authors:
  • Michelle Effros;Hanying Feng;Kenneth Zeger

  • Affiliations:
  • -;-;-

  • Venue:
  • DCC '03 Proceedings of the Conference on Data Compression
  • Year:
  • 2003

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Abstract

We examine the performance of the KLT for transform coding applications.TheKLT 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 approachuses an optimal fixed-rate scalar quantizer to describe the transform coefficients; thevariable-rate approach uses a uniform scalar quantizer followed by an optimal entropycode.Earlier work shows that for the variable-rate case there exist sources on whichthe KLT is not unique and the optimal transform code matched to a "worst" KLT yieldsperformance 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-rateand the variable-rate coding frameworks there exist sources for which the performancepenalty for using a "worst" KLT can be made arbitrarily large.Further, we demonstratein both frameworks that there exist sources for which even a best KLT gives suboptimalperformance.Finally, we show that even for vector sources where the KLT yieldsindependent coefficients, the KLT can be suboptimal for fixed-rate coding.