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On solenoidal-injective and injective ray transforms of tensor fields on surfaces

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arxiv 1807.10730 v2 pith:B3FKSC6R submitted 2018-07-27 math.DG math.AP

Venkateswaran P. Krishnan , Rohit Kumar Mishra , François Monard This is my paper · ORCID
classification math.DGmath.AP
keywords tensortransformsfieldsfirstinjectivesurfacesalonganswer
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We first give a constructive answer to the attenuated tensor tomography problem on simple surfaces. We then use this result to propose two approaches to produce vector-valued integral transforms which are fully injective over tensor fields. The first approach is by construction of appropriate weights which vary along the geodesic flow, generalizing the moment transforms. The second one is by changing the pairing with the tensor field to generate a collection of transverse ray transforms.

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  1. Inverse source problems in transport via attenuated tensor tomography

    math.AP 2019-08 conditional novelty 6.0 of 10

    For simple 2D geometries, the scattering transport inverse source problem is injective for isotropic and vector sources, and the gauge for higher-degree sources is fully described.

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