Image decomposition based on the adaptive direction total variation and \(\mathbb {G}\)-norm regularization


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.

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    Here we set the W with the size \(16\times 16\). \(\tan ^{-1}\) is the arctangent function with output range of \((-\frac{\pi }{2},\frac{\pi }{2})\)


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Correspondence to Zhi-Feng Pang.

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This work was partially supported Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science and Technology, China)

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Shi, B., Meng, G., Zhao, Z. et al. Image decomposition based on the adaptive direction total variation and \(\mathbb {G}\)-norm regularization. SIViP 15, 155–163 (2021).

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  • Image decomposition
  • Cartoon and texture
  • Alternating direction method of multipliers (ADMM)
  • Adaptive direction total variation regularization (ADTV)
  • \(\mathbb {G}\)-norm