Electron. J. Diff. Equ., Vol. 2014 (2014), No. 129, pp. 1-9.

Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model

Tudor Barbu, Angelo Favini

Abstract:
A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explaining the mathematical reasons behind it. Also, we perform a rigorous mathematical investigation on of the existence and uniqueness of the solution of our nonlinear diffusion equation. This PDE-based noise removal approach outperforms most diffusion-based methods, producing considerably better smoothing results and providing a much better edge preservation.

Submitted March 29, 2014. Published June 6, 2014.
Math Subject Classifications: 35Q68, 68U10, 62H35.
Key Words: Edge-preserving image denoising; nonlinear anisotropic diffusion; PDE model; edge-stopping function; diffusivity conductance parameter.

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Tudor Barbu
Institute of Computer Science of the Romanian Academy
Iasi, Romania
email: tudor.barbu@iit.academiaromana-is.ro
Angelo Favini
Department of Mathematics, University of Bologna
Bologna, Italy
email: angelo.favini@unibo.it

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