[IEEE Trans. on Information Theory, August 2004, pp. 1605-1619]
Suboptimality of the Karhunen-Loève Transform for Transform Coding
Michelle Effros, Hanying Feng, and Kenneth Zeger
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 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.
This paper treats fixed-rate and variable-rate transform codes
of non-Gaussian sources.
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,
and each quantized component is encoded separately.
Earlier work shows that for the variable-rate case
there exist sources on which
the KLT is not unique and the optimal quantization and coding stage
matched to a
``worst'' KLT yields performance as much as 1.5 dB worse than the
optimal quantization and coding stage
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 using 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.