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Zbl 1189.94024
Prasath, V.B.Surya; Singh, Arindama
Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising. (English)
[J] J. Appl. Math. 2010, Article ID 763847, 14 p. (2010). ISSN 1110-757X; ISSN 1687-0042/e

Summary: 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.

MSC 2000:: *94A08 Image processing
94A13 Detection theory
68U10 Image processing

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