MARKOV MODELING FOR BAYESIAN RESTORATION OF 2-DIMENSIONAL LAYERED STRUCTURES

Bayesian estimation of two-dimensional stratified structures is described. The major point addressed here is the derivation of a statistical prior model that adequately describes such layered media. This problem is of interest in application domains such as seismic exploration, nondestructive testing, and medical imaging, where the data are generally processed in one dimension only. In order to take local interactions into account, a Markovian description is used. The model is derived so as to fulfill a set of constraints which summarize physical and geometrical characteristics of the problem as well as practical requirements. The approach adopted is reminiscent of the work of Pickard. The resulting class of Markov random fields presents a unilateral structure on a nonrectangular lattice and a hierarchical organization which involves a line process. In addition, it is shown to be an extension of one-dimensional models already used in the application domains previously mentioned. After an investigation of the properties of the model, its practical interest is demonstrated by an application to seismic deconvolution. Simulation results show significant improvements with respect to the usual one-dimensional methods.