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 $\theta$. The parameters ${\alpha }_0$, ${\alpha }_1$ control the Total Generalized Variation (TGV) regularization while the parameter $\theta$ 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.

本文研究了一种新的图像去噪变分优化模型。在这项工作中，提出了一种具有合适数学背景的双层优化技术来自动检测三个关键参数：${\alpha }_0$,${\alpha }_1$和$\theta$. 参数${\alpha }_0$,${\alpha }_1$控制总广义变化（TGV）正则化，而参数$\theta$与各向异性扩散张量有关。正确选择这些参数是一项具有挑战性的任务。由于这些参数总是与图像梯度和纹理的更好近似有关，因此它们的计算在保留图像特征方面起着重要作用。从分析上讲，我们将这些参数的近似结果以及在合适的框架中遇到的双层问题的解决方案包括在内。此外，为了解决偏微分方程约束的最小化问题，提出了一种改进的原始对偶算法。最后，提供了数值结果以消除噪声，同时通过大量比较来保持安全的细节和重要特征，以显示所提出方法的性能。