Single-image blind deblurring with hybrid sparsity regularization

Single-image blind deblurring could be considered as an important preprocessing step in imaging information fusion. Its purpose is to simultaneously estimate blur kernel and latent sharp image from only one observed blurred image. Blind deblurring has been attracting increasing attention in the fields of image processing, computer vision, computational photography, etc. However, it is a typically ill-posed inverse problem, which requires regularization methods to guarantee stable image restoration results. We first proposed to robustly estimate the blur kernels by exploiting non-convex sparsity constraints on image gradients and blur kernels. The corresponding combined non-convex regularization term has the capacity of enhancing estimation accuracy. To guarantee the high-quality non-blind deblurring with estimated blur kernels, the hybrid non-convex first- and second-order TV regularizer was then introduced to stabilize the final image restoration process. The hybrid non-convex regularizer is able to achieve a good balance between sharp edges preservation and undesirable artifacts suppression. The resulting non-convex minimization problems related to blur kernel estimation and non-blind deblurring were handled using efficient numerical optimization algorithms in this paper. Numerous experiments on both synthetic and realistic images have demonstrated the good performance of the proposed blind deblurring method.