A fourth order partial differential equation model from the Weber's total variation for image restoration

2011 ◽  
Author(s):  
Dong-Hong Zhao ◽  
Lai-Sheng Wang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Restoration ◽  
Total Variation ◽  
Fourth Order ◽  
Equation Model ◽  
Order Partial Differential Equation ◽  
Differential Equation Model ◽  
Partial Differential ◽  
Partial Differential Equation Model

Adaptive Fourth Order Partial Differential Equation Filter from the Webers Total Variation for Image Restoration

2013 ◽  
Vol 475-476 ◽  
pp. 394-400
Author(s):  
Dong Hong Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Diffusion Equation ◽  
Image Restoration ◽  
Total Variation ◽  
Laplace Operator ◽  
Fourth Order ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Directed Diffusion

By substituting an anisotropic diffusion operator for the isotropic Laplace operator in the directed diffusion equation, an improvd directed diffusion equation model is proposed. To overcome the staircasing effects and simultaneously avoid edge blurring, this paper proposed an adaptive fourth order partial differential equation from the Webers Total Variation for Image Restoration. This functional is not only to use Laplace operator but also to add the human psychology system, this paper show numerical evidence of the power of resolution of the model with respect to other known models as the Perona-Malik model. Compared results disctincly demonstrate the superiority of our proposed scheme , in terms of removing noise while sharply maintaining the edge features.

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