Recursive Evaluation of Sure for Total Variation Denoising

Abstract

Recently, total variation (TV)-based regularization has become a standard technique for signal denoising. The reconstruction quality is generally sensitive to the value of regularization parameter. In this work, based on Cham-bolle's algorithm, we develop two data-driven optimization schemes based on minimization of Stein's unbiased risk estimate (SURE)-statistically equivalent to mean squared error (MSE). First, we propose a recursive evaluation of SURE to monitor the estimation error during Chambolle's iteration; the optimal value is then identified by the minimum SURE. Second, for fast optimization, we perform alternating update between regularization parameter and solution within Chambolle's iteration. We exemplify the proposed methods with both 1-D and 2-D signal denoising. Numerical experiments show that the proposed methods lead to highly accurate estimate of regularization parameter and nearly optimal denoising performance.