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Inverse Problems and Imaging (IPI)
 

A two-level domain decomposition method for image restoration

Pages: 523 - 545, Volume 4, Issue 3, August 2010      doi:10.3934/ipi.2010.4.523

 
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Jing Xu - Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore (email)
Xue-Cheng Tai - Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore (email)
Li-Lian Wang - Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore (email)

Abstract: 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:  Overlapping domain decomposition, Coarse mesh correction, Total variation minimization, Image restoration.
Mathematics Subject Classification:  68U10, 65M55, 74S20.

Received: August 2009;      Revised: November 2009;      Available Online: July 2010.