Applying Fourth-Order Partial Differential Equations and Contrast Enhancement to Fluorescence Microscopic Image Denoising

2012 ◽  
pp. 123-128 ◽  
Author(s):  
Yu Wang ◽  
Hong Xue
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Contrast Enhancement ◽  
Image Denoising ◽  
Fourth Order ◽  
Microscopic Image ◽  
Partial Differential

scholarly journals Face Image Denoising Method Based on Fourth-Order Partial Differential Equations

2012 ◽  
Vol 6-7 ◽  
pp. 700-703
Author(s):  
Weng Cang Zhao ◽  
Fan Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Image Denoising ◽  
Fourth Order ◽  
Face Image ◽  
Partial Differential ◽  
Denoising Method ◽  
Linear Diffusion ◽  
Non Linear ◽  
Face Image Processing

In order to improve the effect of face image denoising, this paper put forward several face image denoising methods based on partial differential equations, including P-M non-linear diffusion equations and fourth-order partial differential equations. We use those two methods by establishing non-linear diffusion equations and fourth-order anisotropic diffusion partial differential equation. The P-M non-linear diffusion denoising method can remove noise in intra-regions sufficiently but noise at edges can not be eliminated successfully and line-like structures can not be held very well.While the fourth-order partial differential equations denoising can retain the local detail characteristics of the original face image. Finally, through the experimental results we can see the effect of the fourth-order partial differential equations denoising is better, which makes the later face image processing more accurate and promotes the development of face image processing.

scholarly journals Fourth order partial differential equations on general geometries

2006 ◽  
Vol 216 (1) ◽  
pp. 216-246 ◽  
Author(s):  
John B. Greer ◽  
Andrea L. Bertozzi ◽  
Guillermo Sapiro
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Partial Differential

Wavelet Galerkin method for fourth-order multi-dimensional elliptic partial differential equations

2018 ◽  
Vol 16 (05) ◽  
pp. 1850045 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
Gopal Priyadarshi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Computational Cost ◽  
Stability Estimates ◽  
Partial Differential ◽  
Wavelet Galerkin Method

We describe a wavelet Galerkin method for numerical solutions of fourth-order linear and nonlinear partial differential equations (PDEs) in 2D and 3D based on the use of Daubechies compactly supported wavelets. Two-term connection coefficients have been used to compute higher-order derivatives accurately and economically. Localization and orthogonality properties of wavelets make the global matrix sparse. In particular, these properties reduce the computational cost significantly. Linear system of equations obtained from discretized equations have been solved using GMRES iterative solver. Quasi-linearization technique has been effectively used to handle nonlinear terms arising in nonlinear biharmonic equation. To reduce the computational cost of our method, we have proposed an efficient compression algorithm. Error and stability estimates have been derived. Accuracy of the proposed method is demonstrated through various examples.

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