Fast weighted TV denoising via an edge driven metric

In this paper we propose a new Fast Weighted Total Variation denoising approach, where we introduce edge driven weights in the standard TV discrete regularizer and a non Euclidean metric in the discrepancy term, induced by a positive definite matrix B, strictly related to the weights. In this way the fidelity constraint is adapted according to “edgeness” of each pixel. The corresponding minimization problem is iteratively solved by using the Split-Bregman strategy, in which, due to the particular choice of the structure of the positive definite matrix involved in the measure of the fidelity term, the optimality conditions imposed for the computation of the minimum are reduced to simple assignments, since all variables are decoupled. For its solution we propose a Fast Weighted Total Variation (FWTV) algorithm and, moreover, we prove its convergence. Several experiments demonstrate that the FWTV algorithm outperforms, both in terms of accuracy and execution times, the performance of the Weighted Split-Bregman denoising approach, where the ℓ2− norm is used in order to measure the fidelity term. In the case of synthetic images, the proposed algorithm is better respect to the best-state-of-art algorithms, but the methods not based on TV minimization give better performances with respect to our proposal in the case of natural images.