Stabilizing inverse problems by internal data

Peter Kuchment, Dustin Steinhauer

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity and the current) about the parameters of the tissues. This information, in turn, happens to stabilize the exponentially unstable and thus low-resolution optical and electrical impedance tomography. Various known instances of this effect have been studied individually. We show that there is a simple general technique (covering all known cases) that shows what kinds of interior data stabilize the reconstruction, and why. Namely, we show when the linearized problem becomes an elliptic pseudo-differential one, and thus stable. Stability here is meant as the problem being Fredholm, so the local uniqueness is not shown and probably does not hold in such generality. © 2012 IOP Publishing Ltd.
Original languageEnglish (US)
Pages (from-to)084007
JournalInverse Problems
Volume28
Issue number8
DOIs
StatePublished - Jul 30 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The work of PK was partially supported by the NSF DMS grant 0604778. The work of both authors was supported in part by the award number KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST) and by the IAMCS. The authors also wish to thank the referees for their very helpful suggestions and remarks.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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