Serra-Capizzano recently introduced anti-reflecting boundary conditions (AR-BC) for blurring models: the idea seems promising both from the computational and approximation viewpoint. The key point is that, under certain symmetry conditions, the AR-BC matrices can be essentially simultaneously diagonalized by the (fast) sine transform DST I and, moreover, a C1 continuity at the border is guaranteed in the 1D case. Here we give more details for the 2D case and we perform extensive numerical simulations which illustrate that the AR-BC can be superior to Dirichlet, periodic and reflective BCs in certain applications.
A flexible preconditioning approach based on Kronecker product
and singular value decomposition (SVD) approximations is presented. The approach can be used with a variety of boundary conditions, depending on what is most appropriate for the specific deblurring application. It is shown that, regardless of the imposed boundary condition, SVD approximations can be used effectively in filtering methods, such as the truncated SVD, as well as in designing preconditioners for iterative methods.