Constrained Image Deblurring with Sparse Proximal Newton Splitting Method

This chapter proposes a framework of sparse proximal Newton splitting method for constrained image deblurring. This framework can be viewed as a generalization of proximal splitting method, which provides a common update strategy by exploiting second derivative information. This is achieved through utilizing the sparse pattern of inverse Hessian matrix. To alleviate the difficulties of the weighted least squares problem, an approximate solution is derived. Some theoretical aspects related to the proposed method are also discussed. Numerical experiments on various blurring conditions demonstrate the advantage of the proposed method in comparison to other iterative shrinkage-thresholding algorithms.