Boundary conditions and fast deblurring models

Anti-reflecting boundary conditions (AR-BC) for blurring models
were recently introduced (see Serra-Capizzano, SISC, 2003):
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 greater regularity at the border is guaranteed.
We present a technique for combining AR-BC, regularization processes
which are unavoidable when the noise is introduced, and linear algebra
solvers defined ad hoc for the considered structures.
Extensive numerical simulations which illustrate that the AR-BC can be
superior to Dirichlet, periodic and reflective BCs in certain
applications.