Anti-reflective Boundary Conditions and Fast 2D Deblurring Models
M. Donatelli, C. Estatico, J. Nagy,
L. Perrone and S. Serra-Capizzano
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 $C^1$ 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.