Improved block preconditioners for linear systems arising from half-quadratic image restoration

In this paper, the minimization problem with a half-quadratic (HQ) regularization for image restoration is studied. For the structured linear system arising at each step of the Newton method for solving the minimization problem, we propose improved block preconditioners based on approximate inversion of the Schur complement and matrix decomposition of the Hessian matrix. The approximate inverse of the Schur complement is constructed by the Taylor expansion. We analyze the spectral properties of the preconditioned matrix and present eigenvalue bounds. Numerical results illustrate the efficiency of the proposed preconditioners.