Abstract: We propose a novel approach to estimating blur kernel in the Blind Image Deblurring.This is a challenging problem, because image restoration with unknown kernels is an ill-posed deconvolution process.Existing methods are also sensitive to image noise and compression artifacts.Our method overcomes these drawbacks by introducing an adaptive linear filter to handle image noise.The blur kernel is automatically learned together with the adaptive linear filter simultaneously.Then, the clear images are restored using an improved non-blind deblurring method based on reweighted split Bregman iteration optimization.Compared to the state of the arts, our approach is more robust to image noise and shows stable performance in single image deblurring tasks.