A nonlocal weighted difference of anisotropic and isotropic total variation to regularize partition boundaries in an image

In this paper, we propose a new nonlocal model that uses a weighted difference of anisotropic and isotropic total variation (TV) to regularize the partition boundaries in an image. The proposed model integrates the nonlocal operators with the weighted differences of two convex terms, which can exploit the variety nature of textured images to recover all important features and fine detail structures. To solve our proposed model, we apply the difference of convex algorithm (DCA). Then, the subproblems can be minimized by the split-Bregman iteration method introduced in Goldstein and Osher (2009) combined with the Bregmanized Operator Splitting (BOS) method introduced in Zhang et al. (2010). We prove that the sequence generated by the DCA method converges to a stationary point, which satisfies the first-order optimality condition. Various experiments show that the proposed model yields results that can compare favorably with those obtained by various methods in the literature.