Comparison between unitary and causal approaches to backward adaptive transform coding of vectorial signals

Mary, David;Slock, Dirk T M
Research report RR-01-057

In a transform coding framework we compare the optimal causal approach (LDU, Lower-Diagonal-Upper) to the optimal unitary approach (Karhunen-Loeve Transform, KLT). The criterion of merit used for this comparison is the coding gain, defined for a transformation _ as the ratio of the average distortion obtained with identity transformation over the average distortion obtained with _ . In absence of perturbation, both transforms have been recenlty shown to yield the same gain [8, 7]. The purpose of this report is to compare the behavior of these two transformations when the ideal transform coding scheme gets perturbed, that is, when only an estimate _________ _ Of ____ is known. In this case, not only the transformation itself will be perturbated, but also the bit allocation mechanism. We compare the two approaches in three cases. Firstly, is caused by a quantization noise : the coding scheme is based on the statistics of the quantized data. We find that the coding gain in the unitary case is higher than in the causal case. In a second case, _ corresponds to an estimation noise : the coding scheme is based on an estimate of ___ based on a finite amount of available data. In this case, both causal and unitary approaches are strictly equivalent, because of the unimodularity and decorrelating properties of the transformations. Finally, the influence of both perturbations is considered, as this is the case in a real backward adaptive transform coding scheme. Simulations results confirming the predicted behavior of the coding gains with perturbations are reported. The results of this work have been submitted in [2] and [3]. This report is available at .

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