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In many restoration/superresolution applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known. We estimate the PSF and regularization parameters for this ill-posed inverse problem from raw data using the generalized cross-validation method (GCV). To reduce the computational complexity of GCV we propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory. Data-driven blind restoration/superresolution experiments are presented to demonstrate the effectiveness and robustness of our method.