Abstract: A new improved algorithm for image denoising was proposed by analyzing the Total Variational (TV) model. According to the viewpoint of Maximum A Posteriori (MAP) and Markov Random Field (MRF) theory, a generalized variational functional model was deduced. And the Lagrange multiplier λ used for balancing the data fidelity term and regularized term was adaptively improved. An edge preserving potential function was adopted, which had good robustness to noises; finally an iterative algorithm was exploited to solve the energy functional combining weighted gradient descent flow and semi-point scheme. Experimental results show that the proposed model has good performance in image denoising. It is obviously superior to the conventional variational model in both visual effect and PSNR.

Key words: Total Variational (TV) model, Maximum A Posteriori (MAP), Markov Random Field (MRF), Generalized Gaussian Distribution (GGD)

摘要： 通过分析全变分(TV)去噪模型的优缺点，提出了一种新的改进算法。该算法根据最大后验概率(MAP)和马尔可夫随机场(MRF)的理论，推导出一个广义变分的图像去噪模型，并对平衡正则化项和数据保真项的Lagrange乘子λ进行了自适应改进，最后采用了一种鲁棒性好和边缘保持能力强的势函数，结合梯度加权最速下降法和半点格式的数值迭代算法对自适应的广义变分去噪模型寻优求解。实验结果表明，新模型能很好地应用于图像去噪，与现有的算法相比，在峰值信噪比有所提高的同时，图像的主观视觉效果也更好。

关键词: 全变分模型, 最大后验概率, 马尔可夫随机场, 广义高斯分布