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Computational Optimization and Applications

, Volume 54, Issue 2, pp 263–282 | Cite as

Preconditioned iterative regularization in Banach spaces

  • Paola Brianzi
  • Fabio Di Benedetto
  • Claudio Estatico
Article

Abstract

Regularization methods for inverse problems formulated in Hilbert spaces usually give rise to over-smoothness, which does not allow to obtain a good contrast and localization of the edges in the context of image restoration.

On the other hand, regularization methods recently introduced in Banach spaces allow in general to obtain better localization and restoration of the discontinuities or localized impulsive signals in imaging applications.

We present here an expository survey of the topic focused on the iterative Landweber method. In addition, preconditioning techniques previously proposed for Hilbert spaces are extended to the Banach setting and numerically tested.

Keywords

Regularization Banach spaces Landweber method Preconditioning 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Paola Brianzi
    • 1
  • Fabio Di Benedetto
    • 1
  • Claudio Estatico
    • 1
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi di GenovaGenovaItaly
  2. 2.Dipartimento di Scienza ed Alta TecnologiaUniversità degli Studi dell’InsubriaComoItaly

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