Image denoising via a new anisotropic total-variation-based model

Abstract

To keep local structures when denoising the degraded image, we propose a new anisotropic total variation (TV)-based restored model based on the combination of the gradient operator ∇ and the adaptive weighted matrix ,T into the ℓ1-norm regularized term. The weighted matrix ,T depends on the edge indicator function along the x and y-axis directions, so this matrix can rotate the direction of the gradient operator tending to bigger weight and the proposed model can thus describe the local features in image. In order to cope with this nonsmooth model, we employ the alternating direction method of multipliers (ADMM) to solve it. Relying on the convexity, the convergence of the proposed numerical algorithm is provided as well. Denoising experiments on the artificial images and benchmark images show the effectiveness of the proposed model by comparing it to other well-known total-variation-based models in terms of the restored quality.