Mathematical analysis to a nonlinear fourth-order partial differential equation

2011 ◽  
Vol 74 (11) ◽  
pp. 3815-3828 ◽  
Author(s):  
Bo Liang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fourth Order ◽  
Mathematical Analysis ◽  
Order Partial Differential Equation ◽  
Partial Differential

scholarly journals Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yunjiao Bai ◽  
Quan Zhang ◽  
Hong Shangguan ◽  
Zhiguo Gui ◽  
Yi Liu ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Denoising ◽  
Fourth Order ◽  
Objective Evaluation ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
The Difference ◽  
Adaptively Adjusting ◽  
Difference Curvature

The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.

Fourth-order partial differential equation noise removal on welding images

2015 ◽  
Author(s):  
Suhaila Abd Halim ◽  
Arsmah Ibrahim ◽  
Tuan Nurul Norazura Tuan Sulong ◽  
Yupiter HP Manurung
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fourth Order ◽  
Noise Removal ◽  
Order Partial Differential Equation ◽  
Partial Differential

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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