Subspace Information Criterion — Determining Parameters in Linear Filters for Optimal Restoration

We discuss the problem of image restoration from observed images. Most of the image restoration filters proposed so far include parameters that control the restoration properties. For bringing out the optimal restoration performance of the filters, the parameter values should be determined so as to minimize a certain error measure such as the mean squared error (MSE) between the restored image and original image. However, this is not generally possible since the unknown original image itself is required to evaluate MSE. In this paper, we derive an estimator of MSE called the subspace information criterion (SIC), and propose determining the parameter values so that SIC is minimized. It is theoretically shown that, for any linear filter, SIC gives an unbiased estimate of the expected MSE over the noise. Computer simulations with the regularization filter show that SIC tends to outperform existing methods.