Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time

2003 ◽  
Vol 12 (12) ◽  
pp. 1579-1590 ◽  
Author(s):  
M. Lysaker ◽  
A. Lundervold ◽  
Xue-Cheng Tai
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Magnetic Resonance ◽  
Fourth Order ◽  
Noise Removal ◽  
Magnetic Resonance Images ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Space And Time

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

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.

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