4 papers
Geodesic tomography problems on Riemannian manifolds
Jesse Railo
This PhD dissertation is concerned with integral geometric inverse problems. The geodesic ray transform is an operator that encodes the line integrals of a function along geodesics…
Fourier analysis of periodic Radon transforms
Jesse Railo
We study reconstruction of an unknown function from its -plane Radon transform on the flat -torus when . We prove new reconstruction formulas and stability…
Torus computed tomography
Joonas Ilmavirta, Olli Koskela, Jesse Railo
We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT.…
Geodesic ray transform with matrix weights for piecewise constant functions
Joonas Ilmavirta, Jesse Railo
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 comp…