Conclusion

We have briefly presented the essential features of inverse problems, regularization and its Bayesian interpretation. We have confined ourselves to parametric estimation and have only touched on model selection. We stress once again that most classical inversion methods can each be established, or reinterpreted, in several theoretical frameworks, and that there is no exclusive link between methods (more precisely, data processing algorithms) and their theoretical interpretations. The latter, on the other hand, can be classified according to their degree of generality, i.e. their ability to tackle all the problems raised when actually solving an inverse problem.

From this point of view, the Bayesian approach offers a remarkably coherent and complete framework for dealing with inference problems in an uncertain situation where several sources of information are available:...