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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 ...

• 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 ...

• The geodesic X-ray transform with matrix weights 

  Paternain, Gabriel B.; Salo, Mikko; Uhlmann, Gunther; Zhou, Hanming (Johns Hopkins University Press, 2019)

  Consider a compact Riemannian manifold of dimension ≥ 3 with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary ...

• 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 ...

• Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds 

  Ilmavirta, Joonas; Lehtonen, Jere; Salo, Mikko (Cambridge University Press, 2020)

  We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result ...