Nonconvex Variational Model for Space Variant Image Deblurring

In this paper, we mainly study the problem of space variant motion blurred image restoration under general situation, in which the motion blur kernel needs to be estimated before image restoration. According to the optical imaging principle of digital camera, it is found that the rotation motion of the camera around three axes is the main influence factor of the outdoor long distance imaging blur. We use the Gaussian Mixture Model (GMM) and the Mixed Exponential Model (EMM) respectively to fit the gradient distribution of the natural image and the distribution of kernel element of motion blur kernel. Then we solve the relevant parameters in the GMM and EMM by using the Expectation Maximization (EM) Algorithm. We construct the mathematical model for estimation motion blur kernel in the Bayes framework. After estimating the space variant motion blur kernel, by assuming that the noise in the pixel domain and gradient domain both compliance with Gaussian distribution, we add a new regularized constraint to the image restoration model, which can effectively recover the details such as texture contour in the blurred image with the image restoration result converging to the optimal at the same time. Experimental results have demonstrated the satisfactory performance of the proposed method.