Arnoldi methods for image deblurring with anti-reflective boundary conditions

Image deblurring with anti-reflective boundary conditions and a non-symmetric point spread function is considered. Several iterative methods based on Krylov subspace projections, as well as Arnoldi-Tikhonov regularization methods, with reblurring right or left preconditioners are compared. The aim of the preconditioner is not to accelerate the convergence, but to improve the quality of the computed solution and to increase the robustness of the regularization method. Right preconditioning in conjunction with methods based on the Arnoldi process are found to be robust and give high-quality restorations. In particular, when the observed image is contaminated by motion blur, our new method is much more effective than other approaches described in the literature, such as range restricted Arnoldi methods and the conjugate gradient method applied to the normal equations (implemented with the reblurring approach).