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This paper is concerned with developing fast nonrecursive algorithms for the minimum mean-squared error restoration of degraded images. The degradation is assumed to be due to a space invariant, periodic, nonseparable known point-spread function, and additive white noise. Our basic approach is to represent the images by a class of spatial interaction models, namely the simultaneous autoregressve models and the conditional Markov models defined on toroidal lattices, and develop minimum mean-squared error restoration algorithms using these models. The restoration algorithms are optimal, if the parameters characterizing the interaction models are exactly known. However, in practice, the parameters are estimated from the images. By using spatial interaction models, we develop restoration algorithms that do not require the availability of the original image or its prototype. The specific structure of the underlying lattice enables the implementation of the filters using fast Fourier transform (FFT) computations, Several restoration examples are given.