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Article · Inverse Problems and Imaging · January 1, 2010

Reconstructing the metric and magnetic field from the scattering relation

N. S. Dairbekov, Gunther A. Uhlmann

Nurlan Dairbekov
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Abstract

We develop a method for reconstructing the conformal factor of a Riemannianmetric and the magnetic field on a surface from the scattering relation associatedto the corresponding magnetic flow. The scattering relationmaps a starting point and direction of a magnetic geodesic into its end point anddirection. The key point in the reconstruction is the interplay between the magnetic raytransform, the fiberwise Hilbert transform on the circle bundle of the surface,and the Laplace-Beltrami operator of the underlying Riemannian metric.

Numerical methods in inverse problemsSpectral Theory in Mathematical PhysicsGeometric Analysis and Curvature Flowsinverse problemsscattering relationmagnetic field reconstruction

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