Parameters identification for a nonlinear partial differential equation in image denoising

In this work and in the context of PDE constrained optimization problems, we are interested in identification of a parameter in the diffusion equation proposed in [1]. We propose to identify this parameter automatically by a gradient descent algorithm to improve the restoration of a noisy image. Finally, we give numerical results to illustrate the performance of the automatic selection of this parameter and compare our numerical results with other image denoising approaches or algorithms.