Image Denoising Via A New Anisotropic Total-variation-based Model

Image denoising is an important filed in image restoration problems.The high-frequency parts of the image(such as edges,fine textures,etc.)are easily destroyed.In order to overcome this situation,we propose a new anisotropic total variation restored model.In this regularized term,it based on the combination of the gradient operator?and the adaptive weighted matrix T into the?~1-norm regularized term.The weighted matrix depends on the edge indicator function along the x and y-axis direction differences,which enhances the diffusion along the tangential line of the Euler equation corresponding to the model of the isophotes,so this matrix can rotate direction of the gradient operator tending to bigger weight and therefore can describe the local features of the image.In terms of numerical computation,the established model is a non-smooth convex optimization problem which is classical and divisible.we can transforms it into a number of easily solved sub-problems.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 in this thesis as well.In numerical experiments of this thesis,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 approaches in terms of structural similarity index measurement(SSIM).