In this section, we consider the restoration problem, with the aim of restoring noisy images. The main idea is to use the topological gradient for detecting the edges of the noisy image in order to preserve them during the restoration process.
This method is based on thermal diffusion, like many other variational methods. In order to avoid blurring effects, several nonlinear isotropic and anisotropic methods have been introduced, some of them relying on the minimization of the total variation [89,45,78,113,114,13]. We should mention that some non variational approaches also exist, mainly statistical methods [57].
This section summarizes the work presented in [28,25]. We also refer to these references for the results of numerical experiments.