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Analysis and Mathematical Physics

, Volume 4, Issue 3, pp 199–220 | Cite as

On a reconstruction formula for spherical Radon transform: a microlocal analytic point of view

  • Linh V. Nguyen
Article

Abstract

Let \(\mathcal R \) be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface \(\mathcal S \). We study the construction of a function \(f\) from \(\mathcal R (f)\) by a closed-form formula. We approach the problem by studying an oscillatory integral, which depends on the observation surface \(\mathcal S \) as a parameter. We then derive various microlocal analytic properties of the associated closed-form reconstruction formula.

Notes

Acknowledgments

The author is thankful to Professor P. Stefanov for his critical comments to the preliminary version of the article. The author is also thankful to the referee for many helpful comments and suggestions.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IdahoMoscowUSA

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