To improve the decomposition quality, it is very important to describe the local structure of the image in the proposed model. This fact motivates us to improve the Meyer’s decomposition model via coupling one weighted matrix with one rotation matrix into the total variation norm. In the proposed model, the weighted matrix can be used to enhance the diffusion along with the tangent direction of the edge and the rotation matrix is used to make the difference operator couple with the coordinate system of the normal direction and the tangent direction efficiently. With these operations, our proposed model owns the advantage of the local adaption and also describes the image structure robustly. Since the proposed model has the splitting structure, we can employ the alternating direction method of multipliers to solve it. Furthermore, the convergence of the numerical method can be efficiently kept under the framework of this algorithm. Numerical results are presented to show that the proposed model can decompose better cartoon and texture components than other testing methods.

中文翻译：

---

基于自适应方向全变差和$$\mathbb {G}$$-norm 正则化的图像分解

为了提高分解质量，在所提出的模型中描述图像的局部结构非常重要。这一事实促使我们通过将一个加权矩阵与一个旋转矩阵耦合到总变异范数中来改进迈耶分解模型。在所提出的模型中，加权矩阵可用于增强沿边缘切线方向的扩散，旋转矩阵用于使差分算子与法线方向和切线方向的坐标系有效耦合。通过这些操作，我们提出的模型既具有局部自适应的优势，又可以稳健地描述图像结构。由于提出的模型具有分裂结构，我们可以采用乘法器交替方向法来求解。此外，在该算法的框架下，可以有效地保持数值方法的收敛性。数值结果表明，与其他测试方法相比，所提出的模型可以更好地分解卡通和纹理组件。