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Irregularization accelerates iterative regularization

  • Paola Brianzi
  • Fabio Di Benedetto
  • Claudio Estatico
  • Luca Surace
Article
  • 21 Downloads

Abstract

When iterative methods are employed as regularizers of inverse problems, a main issue is the trade-off between smoothing effects and computation time, related to the convergence rate of iterations. Very often, faster methods obtain less accuracy. A new acceleration strategy is presented here, inspired by a choice of penalty terms formerly proposed in 2012 by Huckle and Sedlacek in the context of Tikhonov regularization by direct solvers. More precisely, we consider a special penalty term endowed with high regularization capabilities, and we apply it by using the opposite sign, that is negative, to its regularization parameter. This unprecedented choice leads to an “irregularization” phenomenon, which speeds up the underlying basic iterative method. The speeding up effects of the negative valued penalty term can be controlled through a sequence of decreasing coefficients as the iterations proceed in order to prevent noise amplification, tuning the weight of the correction term which generates the anti-regularization behavior. Filter factor expansion and convergence are analyzed in the simplified context of linear inverse problems in Hilbert spaces, by considering modified Landweber iterations as a first case study.

Keywords

Inverse problems Regularization Modified Landweber Convergence analysis Filter factor 

Mathematics Subject Classification

65F22 65F10 45Q05 

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaGenovaItaly
  2. 2.IPSEOA Marco PoloGenovaItaly

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