Abstract
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.
Highlights
Image restoration is one of the fundamental and challenging tasks in image processing [16, 2], and phenomenal advances have been achieved in variational and PDE-based approaches since the seminal work [43]
The ROF model minimizes the total variation (TV) over the space of bounded variation (BV), so it is capable of preserving sharp edges and boundaries with a high quality recovery
The purpose of this paper is to propose a fast solver based on overlapping domain decomposition and a coarse mesh correction for image processing tasks
Summary
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore, and School of Statistics and Mathematics, Zhejiang Gongshang University, 310018, China.
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