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Regularization is an important method for solving a wide variety of inverse problems in image processing. In order to optimize the reconstructed image, it is important to choose the optimal regularization parameter. The unbiased predictive risk estimator (UPRE) has been shown to give a very good estimate of this parameter. Applying the traditional UPRE is impractical, however, in the case of inverse problems such as deblurring, due to the large scale of the associated linear problem. We propose an approach to reducing the large scale problem to a small problem, significantly reducing computational requirements while providing a good approximation to the original problem.