Sampling and reconstruction of a checkerboard-type random field

A statistical procedure for sampling and reconstructing realizations of a random binary field is developed. The realizations are formed by using two binary Markovian processes defined on two axes. The procedure includes two parts. The first part is the choice of a sampling interval on the basis of a given probability of missing a state. The second part is to construct an estimator for the state transition points and to evaluate the variance of the estimator. The issue of the uncertainty of the initial state is resolved, which arises because the values of the generating processes are nonuniquely determined by field measurements. Illustrative examples are given.