Blind motion deblurring from a single image using sparse approximation

Restoring a clear image from a single motion-blurred image due to camera shake has long been a challenging problem in digital imaging. Existing blind deblurring techniques either only remove simple motion blurring, or need user interactions to work on more complex cases. In this paper, we present an approach to remove motion blurring from a single image by formulating the blind blurring as a new joint optimization problem, which simultaneously maximizes the sparsity of the blur kernel and the sparsity of the clear image under certain suitable redundant tight frame systems (curvelet system for kernels and framelet system for images). Without requiring any prior information of the blur kernel as the input, our proposed approach is able to recover high-quality images from given blurred images. Furthermore, the new sparsity constraints under tight frame systems enable the application of a fast algorithm called linearized Bregman iteration to efficiently solve the proposed minimization problem. The experiments on both simulated images and real images showed that our algorithm can effectively removing complex motion blurring from nature images.