The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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THE METHOD OF NONFLAT TIME EVOLUTION (MONTE) IN PDE-BASED IMAGE RESTORATION

  • Cha, Youngjoon (Department of Applied Mathematics, Sejong University) ;
  • Kim, Seongjai (Department of Mathematics and Statistics, Mississippi State University)
  • Received : 2012.09.26
  • Accepted : 2012.11.08
  • Published : 2012.11.30
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Abstract

This article is concerned with effective numerical techniques for partial differential equation (PDE)-based image restoration. Numerical realizations of most PDE-based denoising models show a common drawback: loss of fine structures. In order to overcome the drawback, the article introduces a new time-stepping procedure, called the method of nonflat time evolution (MONTE), in which the timestep size is determined based on local image characteristics such as the curvature or the diffusion magnitude. The MONTE provides PDE-based restoration models with an effective mechanism for the equalization of the net diffusion over a wide range of image frequency components. It can be easily applied to diverse evolutionary PDE-based restoration models and their spatial and temporal discretizations. It has been numerically verified that the MONTE results in a significant reduction in numerical dissipation and preserves fine structures such as edges and textures satisfactorily, while it removes the noise with an improved efficiency. Various numerical results are shown to confirm the claim.

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