Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds
Hoop, M. V. d., & Ilmavirta, J. (2017). Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds. Inverse Problems, 33 (12), 124003. doi:10.1088/1361-6420/aa9423
Julkaistu sarjassa
Inverse ProblemsPäivämäärä
2017Oppiaine
MatematiikkaTekijänoikeudet
© 2017 IOP Publishing Ltd
We study ray transforms on spherically symmetric
manifolds with a piecewise C
1,1 metric. Assuming the Herglotz
condition, the X-ray transform is injective on the space of L
2
functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a C
1,1 metric. To make these problems tractable in
low regularity, we introduce and study a class of generalized Abel
transforms and study their properties. This low regularity setting
is relevant for geophysical applications.
Julkaisija
Institute of PhysicsISSN Hae Julkaisufoorumista
0266-5611Asiasanat
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
On the broken ray transform
Ilmavirta, Joonas (University of Jyväskylä, 2014) -
Spherically symmetric inhomogeneous cosmological models
Pääkkönen, Mikko (University of Jyväskylä, 2014) -
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 ... -
Geodesic Tomography Problems on Riemannian Manifolds
Railo, Jesse (2019)This 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. The dissertation establishes many conditions ... -
Broken ray transform on a Riemann surface with a convex obstacle
Ilmavirta, Joonas; Salo, Mikko (International Press, 2016)We consider the broken ray transform on Riemann surfaces in the presence of an obstacle, following earlier work of Mukhometov. If the surface has nonpositive curvature and the obstacle is strictly convex, we show that a ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.