Relaxation Methods for Image Denoising Based on Difference Schemes

In this paper, we propose some relaxation methods that can be used to design very fast iteration schemes for image denoising based on the total variation model. By using certain techniques from convex optimization, we establish the convergence of the iteration schemes based on these relaxation methods. Furthermore, we provide some empirical formulas for the parameters needed in the denoising model. As a result, we are able to construct automatic algorithms for image denoising that produce nearly optimal results. Finally, we apply the relaxation methods to image denoising based on high-order difference schemes. The resulting iteration scheme is fast and yields significantly better image quality than the numerical schemes based on the total variation model.