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 sarjassaInverse Problems
© 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.
JulkaisijaInstitute of Physics
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Ilmavirta, Joonas (University of Jyväskylä, 2014)
Pääkkönen, Mikko (University of Jyväskylä, 2014)
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 ...
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 ...
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 ...