Image reconstruction and restoration using the simplified topological e-algorithm

Image reconstruction and restoration using the simplified topological e-algorithm

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Article ID: iaor201530789
Volume: 274
Start Page Number: 539
End Page Number: 555
Publication Date: Feb 2016
Journal: Applied Mathematics and Computation
Authors: ,
Keywords: approximation, image processing, image registration, regularisation techniques, topology
Abstract:

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 e‐algorithm applied to slow‐converging iterative regularization methods. The results of many numerical experiments and comparisons with other methods are also displayed.

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