MARKOV MODELING FOR BAYESIAN RESTORATION OF 2-DIMENSIONAL LAYERED STRUCTURES

Bayesian estimation of two-dimensional stratified structures is descri bed. The major point addressed here is the derivation of a statistical prior model that adequately describes such layered media. This proble m is of interest in application domains such as seismic exploration, n ondestructive testing, and medical imaging, where the data are general ly processed in one dimension only. In order to take local interaction s into account, a Markovian description is used. The model is derived so as to fulfill a set of constraints which summarize physical and geo metrical characteristics of the problem as well as practical requireme nts. The approach adopted is reminiscent of the work of Pickard. The r esulting class of Markov random fields presents a unilateral structure on a nonrectangular lattice and a hierarchical organization which inv olves a line process. In addition, it is shown to be an extension of o ne-dimensional models already used in the application domains previous ly mentioned. After an investigation of the properties of the model, i ts practical interest is demonstrated by an application to seismic dec onvolution. Simulation results show significant improvements with resp ect to the usual one-dimensional methods.