Damped second order flow applied to image denoising
Abstract In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementa...
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| Published in | IMA journal of applied mathematics Vol. 84; no. 6; pp. 1082 - 1111 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Oxford University Press
27.12.2019
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| Online Access | Get full text |
| ISSN | 0272-4960 1464-3634 1464-3634 |
| DOI | 10.1093/imamat/hxz027 |
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| Abstract | Abstract
In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer–Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF. |
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| AbstractList | In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer–Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF. Abstract In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Störmer–Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF. In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of an image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the Stormer-Verlet method, a discrete DF, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the efficiency of SV-DDF. |
| Author | Baravdish, G Svensson, O Gulliksson, M Zhang, Y |
| Author_xml | – sequence: 1 givenname: G surname: Baravdish fullname: Baravdish, G organization: Department of Science and Technology, Linköping University, 58183 Linköping, Sweden – sequence: 2 givenname: O surname: Svensson fullname: Svensson, O organization: Department of Science and Technology, Linköping University, 58183 Linköping, Sweden – sequence: 3 givenname: M surname: Gulliksson fullname: Gulliksson, M organization: School of Science and Technology, Örebro University, 70182 Örebro, Sweden – sequence: 4 givenname: Y surname: Zhang fullname: Zhang, Y email: ye.zhang@smbu.edu.cn organization: Shenzhen MSU-BIT University, 518172 Shenzhen, China, and School of Mathematics and Statistics, Beijing Institude of Technology, 100081 Beijing, China |
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| Keywords | parabolic inverse problems regularization damped Hamiltonian system symplectic method Störmer–Verlet image denoising nonlinear flow Laplace Stormer-Verlet p-parabolic p-Laplace |
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In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a... In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of... |
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| SubjectTerms | damped Hamiltonian system image denoising inverse problems Nonlinear flow p-Laplace p-parabolic regularization Störmer–Verlet symplectic method |
| Title | Damped second order flow applied to image denoising |
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