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Showing 1 to 2 of 2 for “"Non-abelian X-ray transform"”.
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The broken non-abelian X-ray transform and inverse problems for connections at high fixed frequency
… The main inverse problem we study is the broken non-abelian X-ray transform. Given a connection A, its broken non-abelian X-ray transform is given by its parallel transports over a set of broken geodesics that start and end on the boundary. Here, a broken geodesic is a piecewise smooth curve …
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Stability, Range and Statistical Aspects of non-Abelian X-ray tomography
The non-Abelian X-ray transform on a Riemannian manifold with boundary (M,g) is a nonlinear map A → CA that associates to a matrix-valued and possibly direction-dependent function A, referred to as attenuation, its scattering data CA. The scattering data records initial-to-end-value maps for the …