Noise Models For Ill-Posed Problems

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.

Publication Date

9-15-2015

Publication Title

Handbook of Geomathematics: Second Edition

Number of Pages

1633-1658

Document Type

Article; Book Chapter

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/978-3-642-54551-1_24

Socpus ID

84956469651 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84956469651

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