A two-level domain decomposition method for image restoration
Jing Xu, Xue‐Cheng Tai, Li-Lian Wang · Inverse Problems and Imaging · 2010
Image restoration has drawn much attention in recent years and asurge of research has been done on variational models and theirnumerical studies. However, there remains an urgent need todevelop fast and robust methods for solving the minimizationproblems and the underlying nonlinear PDEs to process images ofmoderate to large size. This paper aims to propose a two-leveldomain decomposition method, which consists of an overlapping domaindecomposition technique and a coarse mesh correction, for directlysolving the total variational minimization problems. The iterativealgorithm leads to a system of small size and better conditioningin each subspace, and is accelerated with a piecewise linear coarsemesh correction. Various numerical experiments and comparisonsdemonstrate that the proposed method is fast and robust particularlyfor images of large size.