On statistical reconstruction of random fields and the art of forgery

The problem of statistical reconstruction of Gaussian random fields is considered. It is shown that the reconstruction is made up of the deterministic (predictable and hence unique) component and the stochastic (unpredictable and hence nonunique) component. The reconstruction procedure is briefly sketched for general homogeneous random fields. It is shown that major computational simplifications can be achieved if the unilateral conditional Markov (CM) model of the field is adopted. For CM fields, the possibility of decomposing the restoration procedure into a number of computationally less demanding sub-problems is discussed.