基于分数阶原始对偶模型的图像去噪方法

An Image Denoising Method Based on Fractional Order Primal-Dual Model

图像去噪处理过程中,既要消除噪声又要保留图像边缘特征是很难实现的。为解决此问题,本文在ROF模型的基础上,结合对偶和分数阶理论,提出了一种分数阶原始对偶去噪模型。从结构上分析了分数阶原始对偶去噪模型与鞍点优化模型的相似性,并提出了一种基于预解式的原始对偶数值计算方法,用于模型求解。同时推导出了算法的收敛条件,并基于Morozov原理实现了模型正则化参数的自适应选取。最后,进行了数值实验。实验结果表明:基于分数阶的原始对偶模型能够改善图像的视觉效果,避免造成"阶梯效应",而且能够较好地保留图像的细节信息;基于预解式的原始对偶数值计算方法在一定的参数范围内能够快速收敛。

In the process of image denoising,it is difficult to eliminate image noise with keeping image edge characters. To solve this problem,a fractional order primal-dual denoising model is proposed on the basis of ROF model.The structural similarity between the saddle-point optimization model and this fractional order primal-dual model is analyzed. At the same time,a primal-dual algorithm based on resolvent for solving the saddle-point problem is proposed and it is used for solving the proposed model. The convergence condition of the algorithm is deduced and a regularization parameter adaptive selection method is obtained based on the principle of Morozov. Finally,numerical experiments are carried out. The experiment results show that the proposed model can improve the image visual effect effectively and can well reserve the detail of the image information. And the adoptive primal-dual numerical calculation method has faster convergence speed.