Bi-l0-l2-norm regularization for blind motion deblurring

• A simple blur-kernel estimation method is developed for blind motion deblurring.
• The method is regularized by the newly proposed bi-l0-l2-norm regularization.
• The sharp image and the blur-kernel are estimated very efficiently using FFT.
• Leading performance is achieved in both terms of speed and output quality.

In blind motion deblurring, leading methods today tend towards highly non-convex approximations of the l0-norm, especially in the image regularization term. In this paper, we propose a simple, effective and fast approach for the estimation of the motion blur-kernel, through a bi-l0-l2-norm regularization imposed on both the intermediate sharp image and the blur-kernel. Compared with existing methods, the proposed regularization is shown to be more effective and robust, leading to a more accurate motion blur-kernel and a better final restored image. A fast numerical scheme is deployed for alternatingly computing the sharp image and the blur-kernel, by coupling the operator splitting and augmented Lagrangian methods. Experimental results on both a benchmark image dataset and real-world motion blurred images show that the proposed approach is highly competitive with state-of-the-art methods in both deblurring effectiveness and computational efficiency.