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2010, Volume 4, Issue 3: 523-545. Doi: 10.3934/ipi.2010.4.523
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A two-level domain decomposition method for image restoration

  • 1.

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

Received:  July 31, 2009
Revised:  October 31, 2009
Published:  July 2010
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: 68U10, 65M55, 74S20.

    Citation:
    shu

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