Showing items with similar title or keywords.

• 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 ...