Bayesian methods for image restoration and reconstruction: application to gammagraphy and photofission tomography.

Summary This thesis is devoted to the development of Bayesian algorithms for the solution of inverse problems encountered in gamma radiography and photofission tomography. For each of these applications, the different statistical transformations undergone by the signal and due to the measurement system have been studied. Two possible modelizations of the measurement system have been determined for each of the applications: a relatively simple classical modelization and a new modelization based on cascade point processes. Bayesian em (expectation-maximization) and mcmc (markov chain monte carlo) algorithms for image restoration and reconstruction, based on these modelizations, have been developed and compared. It appeared experimentally that the modeling by cascade point processes does not significantly improve the results obtained from a classical modeling. In the context of gamma radiography, we then proposed two original approaches allowing an improvement of the results. The first one consists in introducing an inhomogeneous markov field as an a priori law, i.e. to vary spatially the regularization parameter associated with a classical Gaussian markov field. However, the estimation of the hyperparameters necessary for this approach remains a major problem. In the context of point source deconvolution, a second approach consists in introducing high level models. The image is modeled by a list of objects with known shapes but unknown number and parameters. The estimation is then performed using reversible jump CMM methods. This approach allows to obtain more accurate results than those obtained by a Markovian field modeling for reduced computation time.