Noise Models for Ill-Posed Problems

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


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.


Regularization Parameter Noise Model Source Condition Tikhonov Regularization Fredholm Integral Equation 
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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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