Approximations for modulus of gradients and their applications to neighborhood filters  

作　　者：Yan CHEN Zhuangji WANG Kewei ZHANG 

机构地区：[1]College of Resource and Environment, China Agricultural University, Beijing 100193, China [2]Department of Agronomy, Iowa State University, Ames, IA 50011,USA [3]School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

出　　处：《Frontiers of Mathematics in China》2013年第4期761-782,共22页中国高等学校学术文摘·数学（英文）

摘　　要：We define an integral approximation for the modulus of the gradient ｜ u（x）｜ for functions f： Ω C Rn → R by modifying a classical result due to Calderon and Zygmund. Our integral approximations are more stable than the pointwise defined derivatives when applied to numerical differentiation for discrete data. We apply our results to design and analyse neighborhood filters. These filters correspond to well-behaved nonlinear heat equations with the conductivity decreasing with respect to the modulus of gradient ｜ u（x）｜. We also show some numerical experiments and evaluate the effectiveness of our filters.We define an integral approximation for the modulus of the gradient ｜ u（x）｜ for functions f： Ω C Rn → R by modifying a classical result due to Calderon and Zygmund. Our integral approximations are more stable than the pointwise defined derivatives when applied to numerical differentiation for discrete data. We apply our results to design and analyse neighborhood filters. These filters correspond to well-behaved nonlinear heat equations with the conductivity decreasing with respect to the modulus of gradient ｜ u（x）｜. We also show some numerical experiments and evaluate the effectiveness of our filters.

关 键 词：BMO modulus of gradient harmonic analysis and PDE neighborhood filter image processing 

分 类 号：O221.2[理学—运筹学与控制论] TQ223.121[理学—数学]