Deblurring Methods Using Antireflective Boundary Conditions

In this note we consider the numerical solution of selfadjoint deblurring problems on bounded intervals. For these problems it has recently been shown that appropriate modelling of the solution near the boundary of the interval may significantly improve the numerical reconstructions. Among the alternatives the so-called antireflective boundary condition appears to be the best known choice. Here we develop an appropriate, i.e., stable and efficient implementation of this model in two steps, namely by (i) transforming the problem to homogeneous boundary values, and (ii) using the fast sine transform to solve the transformed problem. This approach allows to incorporate regularization in a very straightforward way. Numerical reconstructions are superior to those obtained with the reblurring method of Donatelli and Serra-Capizzano. Key words. Deblurring problems, boundary conditions, fast sine transform, Tikhonov regularization AMS subject classifications. 65F22, 65R32, 65T50

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Martin Christiansen, Martin Hanke
• Keywords: Antireflective Boundary Condition, Numerical Reconstructions, Problems, SIAMSC 2008