Abstract: Iterative techniques for image restoration are flexible and easy to implement. The major drawback of iterative image restoration is that the algorithms are often slow in converging to a solution, and the convergence point is not always the best estimate of the original image. Ideally, the restoration process should stop when the restored image is as close to the original image as possible. Unfortunately, the original image is unknown, and therefore no explicit fidelity criterion can be computed. The generalized cross-validation (GCV) criterion performs well as a regularization parameter estimator, and stopping an iterative restoration algorithm before convergence can be viewed as a form of regularization. Therefore, we have applied GCV to the problem of determining the optimal stopping point in iterative restoration. Unfortunately, evaluation of the GCV criterion is computationally expensive. Thus, we use a computationally efficient estimate of the GCV criterion after each iteration as a measure of the progress of the restoration. Our experiments indicate that this estimate of the GCV criterion works well as a stopping rule for iterative image restoration.!15
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