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Injectivity results for the geodesic ray transform
PublisherUniversity of Jyväskylä
ISSN Search the Publication Forum1457-8905
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- Väitöskirjat 
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Geodesic ray transform with matrix weights for piecewise constant functions Ilmavirta, Joonas; Railo, Jesse (Suomalainen tiedeakatemia, 2020)We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and ...
X-ray Transforms in Pseudo-Riemannian Geometry Ilmavirta, Joonas (Springer US, 2018)We study the problem of recovering a function on a pseudo-Riemannian manifold from its integrals over all null geodesics in three geometries: pseudo-Riemannian products of Riemannian manifolds, Minkowski spaces, and tori. ...
The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds Ilmavirta, Joonas; Mönkkönen, Keijo (Springer Science and Business Media LLC, 2023)We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce ...
Unique Continuation Results for Certain Generalized Ray Transforms of Symmetric Tensor Fields Agrawal, Divyansh; Krishnan, Venkateswaran P.; Sahoo, Suman Kumar (Springer Science and Business Media LLC, 2022)Let Im denote the Euclidean ray transform acting on compactly supported symmetric m-tensor field distributions f, and I∗m be its formal L2 adjoint. We study a unique continuation result for the operator Nm=I∗mIm. More ...
Optimal recovery of a radiating source with multiple frequencies along one line Brander, Tommi; Ilmavirta, Joonas; Piiroinen, Petteri; Tyni, Teemu (American Institute of Mathematical Sciences (AIMS), 2020)We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam ...