Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising
We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. By incorporating edges found at multiple scales via an adaptive edge detector-based indicat...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2010/763847 |
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| author | V. B. Surya Prasath Arindama Singh |
| author_facet | V. B. Surya Prasath Arindama Singh |
| author_sort | V. B. Surya Prasath |
| collection | DOAJ |
| description | We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of
anisotropic diffusion. By incorporating edges found at multiple scales
via an adaptive edge detector-based indicator function, the proposed
scheme removes noise while respecting salient boundaries. We create
a smooth transition region around probable edges found and reduce
the diffusion rate near it by a gradient-based diffusion coefficient. In
contrast to the previous anisotropic diffusion schemes, we prove the
well-posedness of our scheme in the space of bounded variation. The
proposed scheme is general in the sense that it can be used with any
of the existing diffusion equations. Numerical simulations on noisy
images show the advantages of our scheme when compared to other
related schemes. |
| format | Article |
| id | doaj-art-c38b95814f684f8f8f8bc25b4118f997 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c38b95814f684f8f8f8bc25b4118f9972025-02-03T00:59:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422010-01-01201010.1155/2010/763847763847Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image DenoisingV. B. Surya Prasath0Arindama Singh1Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, IndiaDepartment of Mathematics, Indian Institute of Technology Madras, Chennai 600036, IndiaWe study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. By incorporating edges found at multiple scales via an adaptive edge detector-based indicator function, the proposed scheme removes noise while respecting salient boundaries. We create a smooth transition region around probable edges found and reduce the diffusion rate near it by a gradient-based diffusion coefficient. In contrast to the previous anisotropic diffusion schemes, we prove the well-posedness of our scheme in the space of bounded variation. The proposed scheme is general in the sense that it can be used with any of the existing diffusion equations. Numerical simulations on noisy images show the advantages of our scheme when compared to other related schemes.http://dx.doi.org/10.1155/2010/763847 |
| spellingShingle | V. B. Surya Prasath Arindama Singh Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising Journal of Applied Mathematics |
| title | Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising |
| title_full | Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising |
| title_fullStr | Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising |
| title_full_unstemmed | Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising |
| title_short | Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising |
| title_sort | well posed inhomogeneous nonlinear diffusion scheme for digital image denoising |
| url | http://dx.doi.org/10.1155/2010/763847 |
| work_keys_str_mv | AT vbsuryaprasath wellposedinhomogeneousnonlineardiffusionschemefordigitalimagedenoising AT arindamasingh wellposedinhomogeneousnonlineardiffusionschemefordigitalimagedenoising |