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  • Research Article
  • Open Access

Regularizing Inverse Preconditioners for Symmetric Band Toeplitz Matrices

EURASIP Journal on Advances in Signal Processing20072007:085606

https://doi.org/10.1155/2007/85606

  • Received: 22 September 2006
  • Accepted: 16 March 2007
  • Published:

Abstract

Image restoration is a widely studied discrete ill-posed problem. Among the many regularization methods used for treating the problem, iterative methods have been shown to be effective. In this paper, we consider the case of a blurring function defined by space invariant and band-limited PSF, modeled by a linear system that has a band block Toeplitz structure with band Toeplitz blocks. In order to reduce the number of iterations required to obtain acceptable reconstructions, in 13 an inverse Toeplitz preconditioner for problems with a Toeplitz structure was proposed. The cost per iteration is of operations, where is the pixel number of the 2D image. In this paper, we propose inverse preconditioners with a band Toeplitz structure, which lower the cost to and in experiments showed the same speed of convergence and reconstruction efficiency as the inverse Toeplitz preconditioner.

Keywords

  • Information Technology
  • Linear System
  • Iterative Method
  • Quantum Information
  • Regularization Method

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Authors’ Affiliations

(1)
Istituto di Informatica e Telematica (IIT), CNR, Via G. Moruzzi 1, Pisa, 56124, Italy
(2)
Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/A, Parma, 43100, Italy
(3)
Dipartimento di Informatica, Università di Pisa, Largo Pontecorvo 3, Pisa, 56127, Italy

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Copyright

© P. Favati et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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