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

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: alpha 0, alpha 1 and 0. The parameters alpha 0, alpha 1 control the Total Generalized Variation (TGV) regularization while the parameter 0 is related to the anisotropic diffusive tensor. A proper selection of these parameters repre-sents a challenging task. Since these parameters are always related to a better approxima-tion 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 parame-ters 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 simulta-neously keep safe fine details and important features with numerous comparisons to show the performance of the proposed approach.(c) 2022 Elsevier Inc. All rights reserved.