In this paper, a novel non-convex fractional-order image denoising model is proposed to suppress the staircase effect produced by the TV model while maintaining a neat contour. The model combines quasi-norm and fractional-order regularization, and employs a diffusion coefficient with a faster convergence rate to preserve more image edges and details. Additionally, an adaptive regularization parameter is designed to adjust the denoising performance of the algorithm. To obtain the optimal approximate solution of the model, an enhanced primal-dual algorithm is adopted and the complexity and convergence of the algorithm are theoretically analyzed. Finally, the effectiveness of the proposed method is demonstrated through numerical experiments.

中文翻译：

---

基于非凸函数的自适应分数阶正则化原对偶图像去噪算法

本文提出了一种新颖的非凸分数阶图像去噪模型，以抑制电视模型产生的阶梯效应，同时保持整齐的轮廓。该模型结合了拟范数和分数阶正则化，并采用收敛速度更快的扩散系数来保留更多的图像边缘和细节。此外，还设计了自适应正则化参数来调整算法的去噪性能。为了获得模型的最优近似解，采用增强的原对偶算法，并从理论上分析了算法的复杂度和收敛性。最后，通过数值实验证明了所提方法的有效性。