In a number of engineering topics we are faced with the inverse problem of recovering the spatial distribution of some scalar or vector quantity from measurements of the interaction of an investigated medium with an incident wave. The common feature of such image reconstruction problems is that they are often ill-posed or ill-conditioned. We review first the basic aspects of standard regularization theory. Then, using an information-based approach, we show that existing regularization criteria, which were introduced in the literature using very different approaches, can be interpreted as special cases of an entropy, in spite of their apparent variety. Finally, we discuss its limitations adn present the Bauyesian statistical approach which allows local properties to be introduced in the estimated image through Markov random fields and associated local energy functions.
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