Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (6): 1771-1784.

• Articles • Previous Articles     Next Articles

A Forward and Backward Diffusion Model for Gray Level Image Restoration

  

  1. Institute of Applied Physics and Computational Mathematics, Beijing 100094
  • Received:2007-12-07 Revised:2009-06-14 Online:2009-12-25 Published:2009-12-25
  • Supported by:

    国家自然科学基金NSF(10531040, 10971244)、中国工程物理研究院与国家自然科学基金委联合基金NSAF(10576013)和中国工程物理研究院科学技术发展基金(2009B0202020)资助

Abstract:

In this paper, a spacially adaptive smoothing and enhancing partial differential equation for image restoation,
 is presented, which is  coupled with time-delay regularization. In order to reverse the process of image degradation, a newly defined shock filter for edge enhancement is incorporated with a level set motion based equation for noise removal. The balance between the two processes is achieved by an edge discrimination function, which is coupled with time-delay regularization, for distinguishing boundary areas and homogeneous regions in  given images. The proposed model is well-posed in terms of viscosity solutions: the existence and
uniqueness of periodic viscosity solution to the initial value problem of the equation is established. Numerical examples of some kinds of images are presented for illuminaating the efficiency of the proposed model.

Key words: Image smoothing and sharpening, Parabolic-hyperbolic equation, Shock filter, Periodic viscosity solution, Time-delay regularization, Level set motion

CLC Number: 

  • 35M10
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