Suboptimality of the Karhunen–LoÈve Transform for Transform Coding

Abstract

Abstract-We examine the performance of the Karhunen-Loève transform (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.

A GMM/CPSO speech recognition system

“…The use of DCT in data compression and pattern classification has been increased in recent years, mainly due to the fact its performance is much closer to the results obtained by the Karhunen-Loève transform which is considered optimal for a variety of criteria such as mean square error of truncation and entropy [4], [5]. This paper demonstrates the potential of DCT, CPSO and GMM in speech recognition and the viability of them [6].…”

Graph-based transforms for inter predicted video coding

“…5. Since x follows a Gaussian mixture distribution, the KLT obtained from the covariance of x (which implicitly performs a second-order approximation of the distribution) is suboptimal in MSE sense [50]. Especially, with many possible image edge locations and different orientations, the underlying distribution may contain a large number of mixtures (i.e., a large M ), which makes learning a model from average statistics inefficient.…”

Astronomical Image Compression Techniques Based on ACC and KLT Coder

“…We can compare it with algorithms based on the unique properties of wavelets and fractals as alternative coding methods [13]. The technique described in this paper has the lossy coder of the spectral coefficients of the Karhunen-Loève transform [11,5]. It seems to be a better solution.…”