Nonconvex Second-Order Variational Image Denoising Model with Adaptive Selection of Regularization Parameters

Image denoising is a typically ill-conditioned inverse problem, which has attracted much attention in the fields of image processing and computer vision. In order to overcome the ill-conditioned nature of this inverse problem, a nonconvex total generalized variation (NTGV)-regularized variational model was proposed in this paper for edge-preserving image denoising. The introduced NTGV regularizer is capable of restoring the degraded images while preserving the fine image details. To further improve the image quality, a local variance-based estimation method was introduced to automatically compute the spatially variant regularization parameters, which can make a good balance between noise suppression and detail preservation. A numerical optimization algorithm based on Alternating Direction Method of Multipliers was proposed to effectively solve the resulting image restoration model. The numerical experiments have been conducted to compare the proposed model with current state-of-the-art image denoising methods. The experimental results have illustrated the good performance of the proposed method.