An optimal bilevel optimization model for the generalized total variation and anisotropic tensor parameters selection

•This paper introduces a bilevel problem for identifying parameters in generalized total variation and anisotropic tensor.•The existence of the solution for the bilevel model has been proved.•A rigorous primal-dual algorithm is applied to the optimization problem to identify the desired parameters.•Representative experiments have been carried-out and many comparison have been checked to show the efficiency of the proposed model. This paper investigates a novel variational optimization model for image denoising. Within this work, a bilevel optimization technique with a suitable mathematical background is proposed to detect automatically three crucial parameters: α0, α1 and θ. The parameters α0, α1 control the Total Generalized Variation (TGV) regularization while the parameter θ is related to the anisotropic diffusive tensor. A proper selection of these parameters represents a challenging task. Since these parameters are always related to a better approximation of the image gradient and texture, their computation plays a major role in preserving the image features. Analytically, we include results on the approximation of these parameters as well as the resolution of the encountered bilevel problem in a suitable framework. In addition, to resolve the PDE-constrained minimization problem, a modified primal-dual algorithm is proposed. Finally, numerical results are provided to remove noise and simultaneously keep safe fine details and important features with numerous comparisons to show the performance of the proposed approach.