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2010 Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising
V. B. Surya Prasath, Arindama Singh
J. Appl. Math. 2010: 1-14 (2010). DOI: 10.1155/2010/763847


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.


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V. B. Surya Prasath. Arindama Singh. "Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising." J. Appl. Math. 2010 1 - 14, 2010.


Published: 2010
First available in Project Euclid: 1 November 2010

zbMATH: 1189.94024
MathSciNet: MR2629836
Digital Object Identifier: 10.1155/2010/763847

Rights: Copyright © 2010 Hindawi

Vol.2010 • 2010
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