Blind image deblurring with unknown boundaries using the alternating direction method of multipliers

Blind image deblurring (BID) is an ill-posed inverse problem, typically solved by imposing some form of regularization (prior knowledge) on the unknown blur and original image. A recent approach, although not requiring prior knowledge on the blurring filter, achieves state-of-the-art performance for a wide range of real-world BID problems. We propose a new version of that method, in which both the optimization problems with respect to the unknown image and with respect to the unknown blur are solved by the alternating direction method of multipliers (ADMM) - an optimization tool that has recently sparked much interest for solving inverse problems, namely due to its modularity and state-of-the-art speed. Our approach also handles seamlessly the realistic case of blind deblurring with unknown boundary conditions. Experiments with synthetic and real blurred images show the competitiveness of the proposed method, both in terms of speed and restoration quality.