A Generalized Variational Image Restoration Model Based on MAP and Robust Estimation

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).