American Institute of Mathematical Sciences

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August  2010, 4(3): 523-545. doi: 10.3934/ipi.2010.4.523

A two-level domain decomposition method for image restoration

Jing Xu 1, , Xue-Cheng Tai 1, and  Li-Lian Wang 1,

1. 

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore, Singapore

Received  August 2009 Revised  November 2009 Published  July 2010

Image restoration has drawn much attention in recent years and a surge of research has been done on variational models and their numerical studies. However, there remains an urgent need to develop fast and robust methods for solving the minimization problems and the underlying nonlinear PDEs to process images of moderate to large size. This paper aims to propose a two-level domain decomposition method, which consists of an overlapping domain decomposition technique and a coarse mesh correction, for directly solving the total variational minimization problems. The iterative algorithm leads to a system of small size and better conditioning in each subspace, and is accelerated with a piecewise linear coarse mesh correction. Various numerical experiments and comparisons demonstrate that the proposed method is fast and robust particularly for images of large size.
Keywords: Coarse mesh correction, Total variation minimization, Image restoration., Overlapping domain decomposition.
Mathematics Subject Classification: 68U10, 65M55, 74S2.
Citation: Jing Xu, Xue-Cheng Tai, Li-Lian Wang. A two-level domain decomposition method for image restoration. Inverse Problems & Imaging, 2010, 4 (3) : 523-545. doi: 10.3934/ipi.2010.4.523
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