Nonlinear image processing: modeling and fast algorithm for regularization with edge detection

This paper deals with edge-preserving regularization. The definition of the regularizing functions and properties such as edge modeling or stability are studied in the variational approach (by minimizing of a criterion) and in the anisotropic diffusion approach (by solving a PDE). We propose sufficient conditions to define an edge-preserving regularizing function, and analyze comparatively several usual functions. We use the algorithm ARTUR based on the half-quadratic transform to solve the nonlinear equation. The image and the edge map are simultaneously estimated