A novel PDE-based image denoising approach is proposed in this paper. One designs here a nonlinear filter for image noise reduction based on the diffusion flow generated by the porous media equation∂u/∂t=Δβ(u), whereβis a nonlinear continuous function of the formβ(u)=λum,0<m<1. With respect to standard 2D Gaussian smoothing and some nonlinear PDE-based filters, this one is more efficient to remove noise from degraded images and also to reduce “staircasing” effects and preserve the image edges.

An anisotropic diffusion-based image enhancement method is proposed in this article. The provided PDE denoising approach is derived from the well-known Perona-Malik nonlinear diffusion model, representing an improved version of it. Thus, we model a novel diffusivity function and explain the mathematical reasons behind it. The conductance parameter of our diffusion technique is automatically detected at each iteration. The proposed PDE-based smoothing technique provides satisfactory noise removal and edge enhancement results, outperforming the most diffusion-based approaches