Geodesic ray transform with matrix weights for piecewise constant functions
Ilmavirta, J., & Railo, J. (2020). Geodesic ray transform with matrix weights for piecewise constant functions. Annales Academiae Scientiarum Fennicae-Mathematica, 45(2), 1095-1102. https://doi.org/10.5186/aasfm.2020.4558
Published inAnnales Academiae Scientiarum Fennicae-Mathematica
DisciplineInversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematics
© the Authors & 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 in dimension three and higher we assume a foliation condition. We make no assumption regarding conjugate points or differentiability of the weight. This extends recent results for unweighted transforms.
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Related funder(s)Academy of Finland
Funding program(s)Postdoctoral Researcher, AoF; Centre of Excellence, AoF
Additional information about fundingJ. I. was supported by the Academy of Finland (decision 295853). J. R. was supported by the Academy of Finland (Centre of Excellence in Inverse Problems Research at the University of Jyväskylä in 2017, Centre of Excellence in Inverse Modelling and Imaging at the University of Helsinki in 2018).
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