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arXiv · 1610.09571

The geodesic X-ray transform with a $GL(n,\mathbb{C})$-connection

François Monard·Gabriel P. Paternain
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Abstract

We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the absence of connection, then for any smooth enough connection multiplied by a complex parameter, the corresponding transform is injective for all values of that parameter outside a discrete set. Range characterizations are also provided, as well as numerical illustrations.

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François Monard, Gabriel P. Paternain. 2016-10-29. The geodesic X-ray transform with a $GL(n,\mathbb{C})$-connection. https://arxiv.org/abs/1610.09571

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