Motion blur kernel estimation in steerable gradient domain of decomposed image

Blind deblurring, typically underdetermined or ill-posed problem, has attracted numerous research studies over the recent years. Various priors of either the image or the blur kernel are proposed to establish various regularization models to estimate the blur kernel. And sharp edges are often employed as an important clue to recover the blur kernel. However, due to the harmful effects caused by textures and various artifacts, sharp edges are not always beneficial to the kernel estimation. To address this problem, this paper presents a step-edge based blind image deblurring algorithm using steerable gradients. The proposed algorithm adopts a coarse-to-fine multiscale framework with step-edge restoration, kernel estimation and latent image estimation. In each scale, the step-edges are detected and refined through fast image decomposition and thresholding on steerable gradients, while the kernel and latent image are estimated by minimizing the quadratic energy functionals with steerable gradients. Because each of the minimizing functional has a closed-form solution, and can be implemented by using FFTs, our algorithm is also very fast. Experimental results on both synthetic and real data demonstrate that our method outperforms most existing single image blind deblurring methods.