Techniques causales de codage avec et sans pertes pour les signaux vectoriels

TL;DRAbstract

This thesis presents and analyzes lossy and lossless coding techniques derived from a general causal framework. In a lossy coding framework firstly, we derive the optimal (linear) transform subject to the constraint of causality. This transform is based optimal prdiction, and corresponds to an LDU (Lower-Diagonal-Upper) factorization of the signal covariance matrix. For a wide range of rates, it is shown to compete with the optimal unitary transform for Gaussian sources, the Karhunen-Loeve transform (KLT). The coding performances of the two transformations are then compared in the framework of adaptive on line transform coding, which is of interest for non stationary sources. In this case, the coding parameters are updated using previously coded/decoded data only. The causal LDU transform is then extended to (matricial) filtering. We show how this decorrelating scheme leads to the notion of generalized MIMO (Multi-Input Multi-Outpu) prediction, in which a certain degree of non causalit

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