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Erschienen in:
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2011 | OriginalPaper | Buchkapitel

Linear Inverse Problems

verfasst von : Charles Groetsch

Erschienen in: Handbook of Mathematical Methods in Imaging

Verlag: Springer New York

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Abstract

This introductory treatment of linear inverse problems is aimed at students and neophytes. An historical survey of inverse problems and some examples of model inverse problems related to imaging are discussed to furnish context and texture to the mathematical theory that follows. The development takes place within the sphere of the theory of compact linear operators on Hilbert space and the singular value decomposition plays an essential role. The primary concern is regularization theory: the construction of convergent well-posed approximations to ill-posed problems. For the most part, the discussion is limited to the familiar regularization method devised by Tikhonov and Phillips.

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Nächstes Kapitel Large-Scale Inverse Problems in Imaging
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Metadaten
Titel
Linear Inverse Problems
verfasst von
Charles Groetsch
Copyright-Jahr
2011
Verlag
Springer New York
Buch
Handbook of Mathematical Methods in Imaging

Print ISBN: 978-0-387-92919-4

Electronic ISBN: 978-0-387-92920-0

Copyright-Jahr: 2011

DOI
https://doi.org/10.1007/978-0-387-92920-0_1