Geodesic
Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model
Electronic journal of differential equations, Tome 2014 (2014)
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.
Classification : 35Q68, 68U10, 62H35
Keywords: edge-preserving image denoising, nonlinear anisotropic diffusion, PDE model, edge-stopping function, diffusivity conductance parameter 
@article{EJDE_2014__2014__a127,
     author = {Barbu,  Tudor and Favini,  Angelo},
     title = {Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1297.35232},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a127/}
}
TY  - JOUR
AU  - Barbu,  Tudor
AU  - Favini,  Angelo
TI  - Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a127/
LA  - en
ID  - EJDE_2014__2014__a127
ER  - 
%0 Journal Article
%A Barbu,  Tudor
%A Favini,  Angelo
%T Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a127/
%G en
%F EJDE_2014__2014__a127
Barbu,  Tudor; Favini,  Angelo. Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a127/