Arnoldi process based on optimal estimation of the regularization parameter

Regularization is an effective method for obtaining satisfactory solutions to super-resolution image restoration problems. The application of regularization necessitates a choice of the regularization parameter as well as the stabilizing functional. However, the best choices are not known a priori for many problems. We present the method of generalized cross-validation (GCV) for obtaining optimal estimates of the regularization parameter from the degraded image data. Implementation of GCV requires costly computation. We use Arnoldi process to reduce the computation so that the GCV criterion can be implemented efficiently. The Arnoldi process can factor the system matrix in super-resolution image restoration into a Hessenberg matrix and orthogonal one. Experiments are presented which demonstrate the effectiveness and robustness of our method.