UPRE method for total variation parameter selection

Total variation (TV) regularization is a popular method for solving a wide variety of inverse problems in image processing. In order to optimize the reconstructed image, it is important to choose a good regularization parameter. The unbiased predictive risk estimator (UPRE) has been shown to give a good estimate of this parameter for Tikhonov regularization. In this paper we propose an extension of the UPRE method to the TV problem. Since direct computation of the extended UPRE is impractical in the case of inverse problems such as deblurring, due to the large scale of the associated linear problem, we also propose a method which provides a good approximation of this large scale problem, while significantly reducing computational requirements.