On the convergence of recursive SURE for total variation minimization

Abstract

Abstract Recently, total variation (TV) regularization has become a standard technique for image recovery. The mean squared error (MSE) of the reconstruction can be reliably estimated by Stein’s unbiased risk estimate (SURE). In this work, we develop two recursive evaluations of SURE, based on Chambolle’s projection method (CPM) for TV denoising and alternating direction method of multipliers (ADMM) for TV deconvolution, respectively. In particular, from the proximal point perspective, we provide the convergence analysis for both iterative schemes and the corresponding Jacobian recursions, in terms of the solution distance, from which follows the convergence of noise evolution of Monte-Carlo simulation in practical computations. The theoretical analysis is supported by numerical examples.