Contribution to restoration of degraded images by a space-variant system: use of an a priori model of the image

Imaging systems often present shift-variant point spread functions which are usually approximated by shift-invariant ones, in order to simplify the restoration problem. The aim of this thesis is to show that, if this shift-variant degradation is taken into account, it may increase strongly the quality of restoration. The imaging system is a pinhole, used to acquire images of high energy beams. Three restoration methods have been studied and compared: the Tikhonov-Miller regularization, the Markov-fields and the Maximum-Entropy methods. These methods are based on the incorporation of an a priori knowledge into the restoration process, to achieve stability of the solution. An improved restoration method is proposed: this approach is based on the Tikhonov-Miller regularization, combined with an a priori model of the solution. The idea of such a model is to express local characteristics to be reconstructed. The concept of parametric models described by a set of parameters (shape of the object, amplitude values,...) is used. A parametric optimization is used to find the optimal estimation of parameters close to the correct a priori information data of the expected solution. Several criteria have been proposed to measure the restoration quality. (author)