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Several state-of-the-art mathematical models useful in image processing are considered. These models include the traditional fast unitary transforms, autoregessive and state variable models as well as two-dimensional linear prediction models. These models introduced earlier ,  as low-order finite difference approximations of partial differential equations are generalized and extended to higher order in the framework of linear prediction theory. Applications in several image Processing problems, including image restoration, smoothing, enhancement, data compression, spectral estimation, and filter design, are discussed and examples given.