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Generalized Solution of Linear Systems and Image Restoration

Author

Listed:
  • F. Aluffi-Pentini

    (Università di Roma-La Sapienza)

  • T. Castrignanò

    (Università di Roma-Tor Vergata)

  • P. Maponi

    (Università di Camerino)

  • V. Parisi

    (Università di Roma-Tor Vergata)

  • F. Zirilli

    (Università di Roma-La Sapienza)

Abstract

Let n, m be positive integers; we consider m×n real linear systems. We define regularized solutions of a linear system as the minimizers of an optimization problem. The objective function of this optimization problem can be seen as the Tikhonov functional when the p-norm is considered instead of the Euclidean norm. The cases p=1 and p=∞ are studied. This analysis is used to restore defocused synthetic images and real images with encouraging results.

Suggested Citation

  • F. Aluffi-Pentini & T. Castrignanò & P. Maponi & V. Parisi & F. Zirilli, 1999. "Generalized Solution of Linear Systems and Image Restoration," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 45-64, October.
  • Handle: RePEc:spr:joptap:v:103:y:1999:i:1:d:10.1023_a:1021717215386
    DOI: 10.1023/A:1021717215386
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    Cited by:

    1. Henryk Gzyl & Noam Zeev, 2002. "Probabilistic Approach to an Image Reconstruction Problem," Methodology and Computing in Applied Probability, Springer, vol. 4(3), pages 279-290, September.

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