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First an investigation of modeling stochastic processes by difference equations (Markov process) was undertaken. The starting point of the modeling procedure is the knowledge of the spectrum of the process. Two methods are discussed. One is based on optimal estimation theory and leads in most cases to a high-order (perhaps infinite) Markov process. The second method, based on linear system theory, leads to a first order Markov process (in matrix representation). Both methods have been extended to two-dimensional processes. Secondly, recursive estimation (filtering) of two-dimensional random fields was addressed. It was shown that a two-dimensional recursive filter cannot be optimal. Therefore, only a sub-optimal solution is available. This solution minimizes the mean square error for a specific structure of a filter. Finally, applications of modeling and recursive filtering are discussed. An image that includes a target, correlated noise and random noise was processed. Some methods of target enhancement (also called 'restoration' are discussed. (Author)