Image Restoration Method Based on Least-Squares and Regularization and Fourth-Order Partial Differential Equations

2010 ◽  
Vol 9 (5) ◽  
pp. 962-967 ◽  
Author(s):  
Xiaoyang Yu ◽  
Yuan Gao ◽  
Xue Yang ◽  
Chu Shi ◽  
Xiukun Yang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Image Restoration ◽  
Least Squares ◽  
Fourth Order ◽  
Partial Differential ◽  
Restoration Method

Image Restoration Based on Partial Differential Equations (PDEs)

2013 ◽  
Vol 647 ◽  
pp. 912-917 ◽  
Author(s):  
Xin Jiang ◽  
Ren Jie Zhang
Keyword(s):  
Quantitative Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Image Restoration ◽  
Development Trend ◽  
Partial Differential ◽  
Image Characteristics ◽  
Restoration Method ◽  
Complex Features ◽  
The Development Trend

Image restoration plays an important role in both the quantitative analysis and qualitative analysis of image. It directly affects the further works of analysis and processing. At present, a large number of image restoration methods are recorded in the literatures. And image restoration method based on partial differential equations(PDEs) is one of the main tools in this area. Although these methods often seem powerless for the images with complex features, image restoration method based on PDEs still has its advantages cannot be replaced. In this paper, we make a summary and appraisal on image restoration methods based on PDEs on basis of the analysis for image characteristics and predict the development trend of image restoration methods based on PDEs.

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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