A sparse proximal Newton splitting method for constrained image deblurring

It is a challenging task to recover a high quality image from the degraded images. This paper proposes a fast image deblurring algorithm. To deal with the limitations of the proximal Newton splitting scheme, a sparse framework is presented, which characterized by utilizing the sparse pattern of the approximated inverse Hessian matrix and relaxing the original assumption on the constant penalty parameter. The proposed framework provides a common update strategy by exploiting the second derivative information. To alleviate the difficulties introduced by the sub-problem of this framework, an approximate solution to the weighted norm based primal-dual problem is derived and studied. Moreover, its theoretical aspects are also investigated. Compared with the state-of-the-art methods in several numerical experiments, the proposed algorithm demonstrates the performance improvement and efficiency.