A unified method for optimizing linear image restoration filters

Image restoration from degraded images lies at the foundation of image processing, pattern recognition, and computer vision, so it has been extensively studied. A large number of image restoration filters have been devised so far. It is known that a certain filter works excellently for a certain type of original image or degradation. However, the same filter may not be suitable for other images, so the selection of filters is exceedingly important in practice. Moreover, if a filter includes adjustable parameters such as the regularization parameter or threshold, its restoration performance relies heavily on the choice of the parameter values. In this paper, we therefore discuss the problem of optimizing the filter type and parameter values. Our method is based on the subspace information criterion (SIC), which is an unbiased estimator of the expected squared error between the restored and original images. Since SIC is applicable to any linear filters, one can optimize the filter type and parameter values in a consistent fashion. Our emphasis in this article is laid on the practical concerns of SIC, such as the noise variance estimation, computational issues, and comparison with existing methods. Specifically, we derive an analytic form of the optimal parameter values for the moving-average filter, which will greatly reduce the computational cost. Experiments with the regularization filter show that SIC is comparable to existing methods in the small degradation case, and SIC tends to outperform existing methods in the severe degradation case.