45 citations · 238 across the 51 of their papers we have counts for
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Analysis and X-ray tomography
Joonas Ilmavirta
These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The…
Tensor tomography in periodic slabs
Joonas Ilmavirta, Gunther Uhlmann
The X-ray transform on the periodic slab , , has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For ten…
Spectral rigidity for spherically symmetric manifolds with boundary
Maarten V. de Hoop, Joonas Ilmavirta, Vitaly Katsnelson
We prove a trace formula for three-dimensional spherically symmetric Riemannian manifolds with boundary which satisfy the Herglotz condition: The wave trace is singular precisely a…
Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds
Joonas Ilmavirta, Jere Lehtonen, Mikko Salo
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…
Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds
Maarten V. de Hoop, Joonas Ilmavirta
We study ray transforms on spherically symmetric manifolds with a piecewise metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2…