Choosing the parameter of image restoration filters by modified subspace information criterion

Practical image restoration filters usually include a parameter that controls regularizability; trade-off between fidelity of a restored image and smoothness of it; and so on. Many criteria for choosing such a parameter have been proposed. However; the relation between these criteria and the squared error of a restored image; which is usually used to evaluate the restoration performance; has not been theoretically substantiated. Sugiyama and Ogawa proposed the subspace information criterion (SIC) for model selection of supervised learning problems and showed that the SIC is an unbiased estimator of the expected squared error between the unknown model function and an estimated one. They also applied it to restoration of images. However, we need an unbiased estimator of the unknown original image to construct the criterion; so it can not be used for general situations. In this paper; we present a modified version of the SIC as a new criterion for choosing a parameter of image restoration filters. Some numerical examples are also shown to verify the efficacy of the proposed criterion.