Image reconstruction and restoration using the simplified topological ε-algorithm

In order to compute meaningful approximations of the solutions of large-scale linear inverse ill-posed problems, some form of regularization should be employed. Cimmino and Landweber methods are well-known iterative regularization methods that can be quite successfully applied for tomographic reconstruction and image restoration problems, despite their usually slow convergence. The goal of this paper is to explore the performance of a recent extrapolation algorithm when applied to accelerate the convergence of these iterative regularization methods. In particular, we provide insight and algorithmic details about the simplified topological ε-algorithm applied to slow-converging iterative regularization methods. The results of many numerical experiments and comparisons with other methods are also displayed.