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Noise Models for Ill-Posed Problems

  • Paul N. Eggermont
  • Vincent LaRiccia
  • M. Zuhair Nashed
Reference work entry

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.

Keywords

Regularization Parameter Noise Model Source Condition Tikhonov Regularization Fredholm Integral Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Paul N. Eggermont
    • 1
  • Vincent LaRiccia
    • 1
  • M. Zuhair Nashed
    • 2
  1. 1.Food and Resource EconomicsUniversity of DelawareNewarkUSA
  2. 2.Department of MathematicsUniversity of Central FloridaOrlandoUSA

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