Image deblurring with an inaccurate blur kernel using a group-based low-rank image prior

We address the problem of restoring an original image from its blurry and noisy observation together with inaccurate information of the blurring process. For this purpose, we propose an enhanced regularized structured total least squares (RSTLS) model that can estimate the latent image and blur kernel simultaneously. In the proposed model, both the image and the blur kernel are characterized by a group-based low-rank prior, which assumes that a group of vectorized similar data patches can be well approximated by a low-rank matrix. We develop an alternating minimization algorithm to solve the proposed model efficiently. Numerical experiments demonstrate the effectiveness of our method in terms of both quantitative measures and visual quality.