HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation
The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constr...
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| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/417486 |
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| author | Shu-Li Mei De-Hai Zhu |
| author_facet | Shu-Li Mei De-Hai Zhu |
| author_sort | Shu-Li Mei |
| collection | DOAJ |
| description | The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed method is independent of the basis function. In this method, a dynamic choice scheme of external grid points is proposed to eliminate the artifacts introduced by the partitioning technique. In order to decrease the calculation amount introduced by the change of the external grid points, the Newton interpolation technique is employed instead of the traditional Lagrange interpolation operator, and the condition number of the discretized matrix different equations is taken into account of the choice of the external grid points. Using the new numerical scheme, the time complexity of the sparse grid method for the image denoising is decreased to O(4J+2j) from O(43J), (j≪J). The experiment results show that the dynamic choice scheme of the external gird points can eliminate the boundary effect effectively and the efficiency can also be improved greatly comparing with the classical interval wavelets numerical methods. |
| format | Article |
| id | doaj-art-be384b8799aa4f69b29c358f81d556ba |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-be384b8799aa4f69b29c358f81d556ba2025-02-03T01:12:38ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/417486417486HPM-Based Dynamic Sparse Grid Approach for Perona-Malik EquationShu-Li Mei0De-Hai Zhu1College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, ChinaKey Laboratory of Agricultural Information Acquisition Technology, Ministry of Agriculture, China Agricultural University, Beijing 100083, ChinaThe Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed method is independent of the basis function. In this method, a dynamic choice scheme of external grid points is proposed to eliminate the artifacts introduced by the partitioning technique. In order to decrease the calculation amount introduced by the change of the external grid points, the Newton interpolation technique is employed instead of the traditional Lagrange interpolation operator, and the condition number of the discretized matrix different equations is taken into account of the choice of the external grid points. Using the new numerical scheme, the time complexity of the sparse grid method for the image denoising is decreased to O(4J+2j) from O(43J), (j≪J). The experiment results show that the dynamic choice scheme of the external gird points can eliminate the boundary effect effectively and the efficiency can also be improved greatly comparing with the classical interval wavelets numerical methods.http://dx.doi.org/10.1155/2014/417486 |
| spellingShingle | Shu-Li Mei De-Hai Zhu HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation The Scientific World Journal |
| title | HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation |
| title_full | HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation |
| title_fullStr | HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation |
| title_full_unstemmed | HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation |
| title_short | HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation |
| title_sort | hpm based dynamic sparse grid approach for perona malik equation |
| url | http://dx.doi.org/10.1155/2014/417486 |
| work_keys_str_mv | AT shulimei hpmbaseddynamicsparsegridapproachforperonamalikequation AT dehaizhu hpmbaseddynamicsparsegridapproachforperonamalikequation |