GENERALIZED CROSS-VALIDATION FOR TOTAL VARIATION IMAGE RESTORATION

Abstract. In this paper, we consider and study total variation (TV) image restoration. In literature, there are several regularization parameter selection methods for Tikhonov regularization problems (e.g., the discrepancy principle and the generalized cross-validation method). However, these selection methods have not been developed for TV regularization problems. The main aim of this paper is to develop a fast TV image restoration method with automatic selection of regularization parameters to restore blurred and noisy images. The method exploits the generalized cross-validation (GCV) technique to determine inexpensively how much regularization used in each restoration step. By updating these regularization parameters in the iterative procedure, the restored image can be obtained by choosing the one having the minimum GCV value. Our experimental results show that the quality of restored images by the proposed method with no prior knowledge of the original image is quite well. We will also demonstrate the proposed method is also very efficient