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On problem of polarization tomography, I

Roman Novikov·Vladimir Sharafutdinov
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Abstract

The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $Dη/dt=π_{\dotγ}fη$ known for every geodesic $γ$ of a given Riemannian metric. Here $π_{\dotγ}$ is the orthogonal projection onto the hyperplan $\dotγ^{\perp}$. The problem arises in optical tomography of slightly anisotropic media. The local uniqueness theorem is proved: a $C^1$- small function f can be recovered from the data uniquely up to a natural obstruction. A partial global result is obtained in the case of the Euclidean metric on $R^3$.

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Roman Novikov, Vladimir Sharafutdinov. 2007-02-23. On problem of polarization tomography, I. https://doi.org/10.1088/0266-5611%2F23%2F3%2F023

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