On a derived non linear model in image restoration

In the process of image restoration, the denoising is an important step. Several models of non-linear diffusive filters requiring solving partial differential equations have been proposed in the literature [1], [2], [3], [4], [5], [6], [7] during the last decades. The existence and uniqueness of a solution in Hilbert space has been established under suitable conditions on the filtering function for the Perona Malik model [5] considering Dirichlet homogeneous and inhomogeneous boundary conditions [1], [2]. In this work, we propose a nonlinear diffusion model inspired by the Perona-Malik one taking into account the Neumann boundary condition. The existence, uniqueness and regularity of the solution to the mathematical problem are established in a Hilbert space. The numerical simulation of the discretized problem is performed using the finite elements method. The effectiveness of this model has been tested on many noisy images with noises of different natures. A comparison of signal to noise ratio (SNR) is used to estimate the quality of the restored images by this model and the Perona-Malik one.