Most of the image restoration filters proposed so far include parameters that control the restoration properties. For bringing out the optimal restoration performance, these parameters 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 for evaluating 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. For any linear filter, SIC gives an unbiased estimate of the expected MSE over the noise. Therefore, the proposed method is valid for any linear filter. Computer simulations with the moving-average filter demonstrate that SIC gives a very accurate estimate of MSE in various situations, and the proposed procedure actually gives the optimal parameter values that minimize MSE.