中文摘要：

基于最大后验概率和MRF理论的图像恢复描述框架,提出一个面向图像恢复的推广变分模型.模型中将噪声建模为广义正态分布,利用最大似然法估计形状参数自动选择合适的范数作为数据保真项;将图像梯度场的分布建模为混合密度类,利用鲁棒估计理论构造一个耦合全变差积分和Dirichlet积分的图像先验模型作为正则化项.利用推广泛函的凸性,讨论了该推广模型的最优解存在性.最后提出结合梯度加权最速下降和半点格式的数值迭代算法.实验结果表明,推广模型能自动区分污染图像中的噪声分布特性,对于高斯噪声和脉冲噪声的污染图像都能取得很好的恢复效果.通过计算峰值信噪比和边缘保护指数,分析和评价了推广模型与目前其他变分方法的性能.

英文摘要：

Starting from the viewpoint of maximum a posteriori （MAP） and MRF theory, a generalized variational functional model for image restoration is established in this paper. In this model, a hybrid image regularization term and image fidelity term are included. For image fidelity term, the distribution of noise is treated as the generalized Gaussian density, and thus the shape parameter is estimated by a maximum likelihood method to automatically choose the suitable L^p norm as the image fidelity criteria. Assuming that the gradient of images is a member of ε-contaminated normal distributions, an image prior model in the form of total variational integral and Dirichlet integral is proposed using the robust estimation method. Due to the convexity of the proposed energy functional, the existence of the minimizing solution of such functional is discussed. Finally a weighted gradient descent flow is developed for image de-noising with an iterative algorithm based on semi-point scheme. Experimental results show that the model can automatically distinguish the statistical distribution of noise and has good performance in image restoration, including Gaussian noise and impulse noise pollution. Compared with other variation methods, the performance analysis and evaluation is made by calculating the peak of signal noise ratio （PSNR） and peak of edge preservation ability （PEPA）.