Image denoising models based on the total variation (TV) regularization have been used in many fields of image processing. The main advantage of the TV regularization can preserve the edge efficiently when restoring the degraded image. However, the main flaw can not describe the local feature due to the same weight for the gradient subvariable in the TV term. To this end, we propose a nonconvex anisotropic total variation (NCATV)-based image denoising model. In the proposed model, the weighted matrix depends on the restored image, so we can expect that it can describe local features to be more robust. Due to the nonconvexity of the proposed model, first we need to use the successive replacement scheme to decouple with the weighted matrix from the TV term. With this operation, the proposed model is transformed into the nonsmooth and convex optimization problem. Then we can employ the alternating direction method of multipliers (ADMM) to transform this problem into several easily solvable subproblems. Numerical experiments show that our proposed model yields an improvement in performance both visually and quantitatively compared with some state-of-the-art methods.

基于总变化量（TV）正则化的图像去噪模型已经在图像处理的许多领域中使用。TV正则化的主要优点是在还原降级图像时可以有效地保留边缘。但是，由于电视术语中的梯度子变量具有相同的权重，因此主要缺陷无法描述局部特征。为此，我们提出了一种基于非凸各向异性总变化量（NCATV）的图像去噪模型。在提出的模型中，加权矩阵取决于恢复的图像，因此我们可以期望它可以描述局部特征，从而更加健壮。由于所提出模型的非凸性，首先我们需要使用连续替换方案将加权矩阵与TV项解耦。通过此操作，将该模型转化为非光滑凸优化问题。然后，我们可以采用乘数的交替方向方法（ADMM）将这个问题转换为几个易于解决的子问题。数值实验表明，与某些最新方法相比，我们提出的模型在视觉和定量方面均具有改进的性能。