Decompositions parcimonieuses: approches Baysiennes et application a la compression d’ image

This thesis interests in different methods of image compression combining both Bayesian aspects and “sparse decomposition” aspects. Two compression methods are in particular investigated. Transform coding, first, is addressed from a transform optimization point of view. The optimization is considered at two levels: in the spatial domain by adapting the support of the transform, and in the transform domain by selecting local bases among finite sets. The study of bases learned with an algorithm from the literature constitutes an introduction to a novel learning algorithm, which encourages the sparsity of the decompositions. Predictive coding is then addressed. Motivated by recent contributions based on sparse decompositions, we propose a novel Bayesian prediction algorithm based on mixtures of sparse decompositions. Finally, these works allowed to underline the interest of structuring the sparsity of the decompositions. For example, a weighting of the decomposition atoms can be considered by the use of a Bernoulli-Gaussian model with different parameters. This model is studied in the last part of this thesis, for the development of sparse decomposition algorithms.