On Anisotropic Variational Model for SAR Image Despeckling

Mostly motivated by practical applications especially in the field of satellite remote sensing of agricultural territories, we develop a novel approach to SAR image despeckling based on minimization of a special anisotropic energy functional. We propose a new statement of this problem in the weighted Sobolev spaces, provide a rigorous mathematical analysis of the proposed optimization problem, establish sufficient conditions of its solvability, show that the objective functional is Gateaux differentiable, and derive the corresponding optimality conditions. To illustrate the validity of the obtained results, we give some examples of numerical simulations with real satellite SAR images