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This paper considers the restoration of images degraded by a motion blur in the presence of noise. Based on a two-dimensional separable autoregressive image model, a one-dimensional horizontally causal vector state space model with multiple delays is derived. By the discrete sine transform, the one-dimensional vector state space model is decomposed into a set of nearly uncorrelated scalar subsystems, to which the Kalman filter is applied to obtain an approximate recursive computationally efficient restoration algorithm for motion degraded images. The same technique is also applied to a semicausal minimum variance image model in order to derive a related recursive restoration algorithm. The computational efficiency is accomplished by the discrete sine transform and the transform data compression technique. Numerical results are presented to show the applicability of the algorithms developed. Finally, the possible extension of the present method to the case of general blur is suggested.