An Extended Sparse Model for Blind Image Deburring

Abstract Blind image deburring is a classical ill-posed problem that usually requires constraints on the clean image, the blur kernel, and noise to make it well-posed. Recently, a simple yet effective sparse norm l e is proposed, which adds two widely-adopted sparse norms, i.e., l 0 and l 1 . By using l e to regularize the gradients of the clean image, and l2 + ∇le as the noise fitting function, an enhanced sparse model for blind image deburring is established and achieves surprisingly attractive results. In this paper, inspired by the facts that the gradients of a natural image tend to obey a heavy-tailed distribution, and the noise exhibits spatial random-ness, we propose a more flexible model called the extended sparse model which can take the enhanced sparse model as a special case. Specifically, for the image gradients, we suggest a improved sparse norm l P , which is developed from l 0 and l p (0 < p ≤ 1). Furthermore, we constrain the second-order derivative of noise to boost the percentage of high-frequencies in the fidelity such that the recovery focuses more on high-frequencies that are erased in the blurry image. Based on the half-quadratic splitting method and a variant of the generalized iterated shrinkage algorithm (GISA), we provide an effective optimization scheme for the overall model. Extensive evaluations of benchmark datasets and real images indicate the superiority of the proposed method against state-of-the-art deburring algorithms.