On effective stopping time selection for visco-plastic nonlinear BV diffusion filters used in image denoising

被引：10
作者：
Frigaard, IA
Ngwa, G
Scherzer, O
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z4, Canada
[2] Univ British Columbia, Dept Mech Engn, Vancouver, BC V6T 1Z4, Canada
[3] Univ Buea, Dept Math, Buea, Cameroon
[4] Univ Innsbruck, Dept Comp Sci, A-6020 Innsbruck, Austria
来源：
SIAM JOURNAL ON APPLIED MATHEMATICS | 2003年 / 63卷 / 06期
关键词：
visco-plastic fluids; nonlinear diffusion filtering; stability; variational methods; image processing;
D O I：
10.1137/S0036139902400465
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider denoising applications using nonlinear diffusion filters of BV type. Using the multiple timescales method, an equation is derived that approximates the time evolution of the image noise. Analysis of the corresponding variational inequality leads to an estimate of the timescale over which the noise decays to its local mean, given in terms of the filter parameters. We present a number of computed examples that demonstrate the validity of our stopping time estimate.
引用
收藏
页码：1911 / 1927
页数：17
相关论文
共 78 条
  • [1] Acar R., Vogel C.R., Analysis of bounded variation penalty methods for ill-posed problems, Inverse Problems, 10, pp. 1217-1229, (1994)
  • [2] Alvarez L., Guichard F., Lions P.-L., Morel J.-M., Axioms and fundamental equations of image processing, Arc. Ration. Mech. Anal., 123, pp. 199-257, (1993)
  • [3] Alvarez L., Lions P.-L., Morel J.-M., Image selective smoothing and edge detection by nonlinear diffusion, II, SIAM J. Numer. Anal., 29, pp. 845-866, (1992)
  • [4] Alvarez L., Morel J.-M., Formalization and computational aspects of image analysis, Acta Numer. 1994, pp. 1-59, (1994)
  • [5] Ambrosio L., Geometric evolution problems, distance function and viscosity solutions, Calculus of Variations and Partial Differential Equations, pp. 5-94, (1999)
  • [6] Ambrosio L., Dancer N., Calculus of Variations and Partial Differential Equations, (1999)
  • [7] Andreu F., Ballester C., Caselles V., Mazon J.M., Minimizing total variation flow, C. R. Acad. Sci. Paris Sér. I Math., 331, pp. 867-872, (2000)
  • [8] Andreu F., Ballester C., Caselles V., Mazon J.M., The Dirichlet problem for the total variation flow, J. Funct. Anal., 180, pp. 347-403, (2001)
  • [9] Andreu F., Ballester C., Caselles V., Mazon J.M., Minimizing total variation flow, Differential Integral Equations, 14, pp. 321-360, (2001)
  • [10] Andreu F., Caselles V., Diaz J.I., Mazon J.M., Some qualitative properties for the total variation flow, J. Funct. Anal., 188, pp. 516-547, (2002)
12345678