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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Inversion of the Radon transform, based on the theory of A-analytic functions, with application to 3D inverse kinematic problem with local data

A. L. Bukhgeim / A. A. Bukhgeim

Department of Mathematics and Statistics, Wichita State University, 1845 N. Fairmount, Wichita, KS, 67260-0033, USA. E-mail:

Schlumberger, Aslakveien 14E, 0753 Oslo, Norway. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 3, Pages 219–234, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406777340883,

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In the introduction we show that the inverse problems for transport equations are naturally reduced to the Cauchy problem for the so called A-analytic functions, and hence the solution is given in terms of operator analog of the Cauchy transform. In Section 2 we develop elements of the theory of A-analytic functions and obtain stability estimates for our Cauchy transform. In Section 3 we discuss numerical aspects of this transformation. In Section 4 we apply this algorithm to the 3-dimensional inverse kinematic problem with local data on the Earth surface, using modified Newton method and discuss numerical examples.

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[1]
Alexandru Tamasan
Inverse Problems, 2007, Volume 23, Number 5, Page 2197

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