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Noise Models for Ill-Posed Problems

In: Handbook of Geomathematics

Author

Listed:
  • Paul N. Eggermont

    (University of Delaware, Food and Resource Economics)

  • Vincent LaRiccia

    (University of Delaware, Food and Resource Economics)

  • M. Zuhair Nashed

    (University of Central Florida, Department of Mathematics)

Abstract

The standard view of noise in ill-posed problems is that it is either deterministic and small (strongly bounded noise) or random and large (not necessarily small). Following Eggerment, LaRiccia and Nashed (2009), a new noise model is investigated, wherein the noise is weakly bounded. Roughly speaking, this means that local averages of the noise are small. A precise definition is given in a Hilbert space setting, and Tikhonov regularization of ill-posed problems with weakly bounded noise is analysed. The analysis unifies the treatment of “classical” ill-posed problems with strongly bounded noise with that of ill-posed problems with weakly bounded noise. Regularization parameter selection is discussed, and an example on numerical differentiation is presented.

Suggested Citation

  • Paul N. Eggermont & Vincent LaRiccia & M. Zuhair Nashed, 2010. "Noise Models for Ill-Posed Problems," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, chapter 24, pages 739-762, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01546-5_24
    DOI: 10.1007/978-3-642-01546-5_24
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