数学物理学报(英文版)

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BV SOLUTIONS TO A DEGENERATE PARABOLIC EQUATION FOR IMAGE DENOISING

孔令海; 郇中丹; 郭柏灵   

  1. 北京应用物理与计算数学研究所, 北京 100088
  • 收稿日期:2004-09-21 修回日期:2005-08-10 出版日期:2007-01-20 发布日期:2007-01-20
  • 通讯作者: 孔令海
  • 基金资助:

    This research is partially supported by NSAF of China (10576013) and by NSFC of China (10531040)

BV SOLUTIONS TO A DEGENERATE PARABOLIC EQUATION FOR IMAGE DENOISING

Kong Linghai; Huan Zhongdan; Guo Boling   

  1. Institute of Applied Physics and Computational Mathematics, P.O.Box 8009-13, Beijing 100088, China
  • Received:2004-09-21 Revised:2005-08-10 Online:2007-01-20 Published:2007-01-20
  • Contact: Kong Linghai

摘要:

In this article, the authors consider equation ut={\rm div}(\varphi (\Gamma u ) A(|D u|2)Du)-(u-I), where $\varphi $ is strictly positive and $\Gamma $ is a known vector-valued mapping, $A: {\Bbb R}_{+}\rightarrow {\Bbb R}^{+}$ is decreasing and $A(s)\sim 1/\sqrt{s} $ as $s\rightarrow +\infty $. This kind
of equation arises naturally from image denoising. For an initial datum $I \in {\rm BV}_{\rm loc}\cap L^{\infty},$ the existence of BV solutions to the initial value problem of the equation is obtained.

关键词: BVloc function, BVx function, strongly degenerate parabolic, denoising

Abstract:

In this article, the authors consider equation ut={\rm div}(\varphi (\Gamma u ) A(|D u|2)Du)-(u-I), where $\varphi $ is strictly positive and $\Gamma $ is a known vector-valued mapping, $A: {\Bbb R}_{+}\rightarrow {\Bbb R}^{+}$ is decreasing and $A(s)\sim 1/\sqrt{s} $ as $s\rightarrow +\infty $. This kind
of equation arises naturally from image denoising. For an initial datum $I \in {\rm BV}_{\rm loc}\cap L^{\infty},$ the existence of BV solutions to the initial value problem of the equation is obtained.

Key words: BVloc function, BVx function, strongly degenerate parabolic, denoising

中图分类号: 

  • 35K65