Noise Models for Ill-Posed Problems

Paul N. Eggermont, Vincent LaRiccia and M. Zuhair Nashed
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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

Chapter 24 in Handbook of Geomathematics, 2010, pp 739-762 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01546-5_24

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DOI: 10.1007/978-3-642-01546-5_24

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