Backward adaptive transform coding of vectorial signals: A comparison between unitary and causal approaches

In a transform coding framework we compare the optimal unitary approach (Karhunen-Loeve Transform, KLT) to the optimal causal approach (LDU, Lower Diagonal-Upper). In absence of perturbations, both transforms have recently been shown to yield the same coding gain [2, 4]. The purpose of this paper is to compare the behavior of these two transformations when the ideal transform coding scheme gets perturbed, that is, when only a perturbed value R_xx + ΔR of R_xx is known at the encoder. In a real backward adaptive scheme, ΔR is due to two noise sources: estimation noise (finite set of available data at the encoder) and quantization noise (quantized data at the decoder) Furthermore, not only the transformation itself gets perturbed, but also the bit assignment. Theoretical expressions for the coding gains in both unitary and causal approaches are derived. Simulation results confirming the predicted behavior of the coding gains with perturbations are reported. This work is a follow-up of [1], where the influences of quantization and estimation noises were analyzed separately.