对图像处理中ROF全变分模型的两种算法的比较研究

Comparative Research on Two Kinds of Algorithms of ROF Total Variational Model in Image Processing

全变分图像去噪问题的本质是一类基于全变分的约束极小化模型.其中最经典的模型是由Rudin-Osher-Fatemi提出的ROF模型[1].在这一模型中,正则化参数的选取直接影响到图像恢复的效果,当给定一个适当的正则化参数来平衡数据拟合和正则解时,可以得到十分理想的结论.在过去的二十年中,通过对这一模型的研究,产生了各种有效的算法.不同的算法通过调节正则化参数,都在不同程度上达到了去噪的目的.本文中,应用两种算法:梯度下降法和分裂Bregman算法,对带噪声图像进行了数值仿真和比较,结果显示分裂Bregman算法能够达到更好地去噪效果.

The variational problem of image denoising is the nature of a class of constrained minimization based on total variational model. The best and most influential example is the Rudin- Osher-Fatmi（ROF） total-variation-based image denoising model. The selection of regularization parameter directly affects the effect of image restoration. Appropriate regularization parameter to balance the data fitting and regular solution can obtain ideal results. In the past twenty years, through the study of this model, various effective algorithms have been proposed. By adjusting the regularization parameter, different algorithms meet the purpose of denoising in different degrees. In this paper, we apply two kinds of algorithms： split Bregman algorithm and the gradient descent method to do numerical simulation and compare them. The results show that the split Bregman algorithm can achieve better denoising effect.