Concave–convex norm ratio prior based double model and fast algorithm for blind deconvolution

A blurred image is usually modeled as the convolution of a sharp image with a blur kernel, so blind image deconvolution is a difficult ill-posed problem since both the blur kernel and the sharp image are unknown. To overcome this difficulty, regularization methods are required to stabilize the solution, which usually utilizes some convex priors to solve an optimization model. Recent theoretical results have demonstrated the superiority of the non-convex sparse prior over the convex counterparts. The non-convex prior, however, leads to a non-convex, non-smooth optimization model that is difficult to solve accurately and efficiently. In this paper, we propose a double model to solve single image blind deconvolution problem. The model consists of 2 cost functions. The first function consists of a L1 data fitting term and a concave–convex norm ratio prior, which is used to estimate the sharp image, the second function consists of a L2 data fitting term and a L1 prior term, which is used to estimate the kernel. We utilize multi-scale analysis method to estimate the blur kernel from coarse to fine. For the non-convex prior, we introduce a split method and a closed-form thresholding formulas to restore the sharp image. This method can obtain fast convergence and get more sharp image. Experimental results on image deblurring verify the effectiveness and efficiency of our model and algorithm. The proposed model and fast algorithm can be easily used in sparse modeling and representation learning.