On the inversion formulas of Pestov and Uhlmann for the geodesic ray transform

2010 ◽  
Vol 18 (4) ◽  
Author(s):  
Venkateswaran P. Krishnan
Keyword(s):  
Inversion Formulas ◽  
Ray Transform ◽  
Geodesic Ray Transform

scholarly journals Sharp stability estimate for the geodesic ray transform

2020 ◽  
Vol 36 (2) ◽  
pp. 025013 ◽  
Author(s):  
Yernat M Assylbekov ◽  
Plamen Stefanov
Keyword(s):  
Stability Estimate ◽  
Ray Transform ◽  
Sharp Stability ◽  
Geodesic Ray Transform

scholarly journals Inverting the local geodesic ray transform of higher rank tensors

2019 ◽  
Vol 35 (11) ◽  
pp. 115009
Author(s):  
Maarten V de Hoop ◽  
Gunther Uhlmann ◽  
Jian Zhai
Keyword(s):  
Ray Transform ◽  
Higher Rank ◽  
Geodesic Ray Transform

Nonlocal inversion formulas for the X-ray transform

1989 ◽  
Vol 58 (1) ◽  
pp. 205-240 ◽  
Author(s):  
Allan Greenleaf ◽  
Gunther Uhlmann
Keyword(s):  
Inversion Formulas ◽  
X Ray ◽  
Ray Transform

scholarly journals A support theorem for the geodesic ray transform of symmetric tensor fields

2009 ◽  
Vol 3 (3) ◽  
pp. 453-464 ◽  
Author(s):  
Venkateswaran P. Krishnan ◽  
◽  
Plamen Stefanov ◽  
Keyword(s):  
Symmetric Tensor ◽  
Tensor Fields ◽  
Support Theorem ◽  
Ray Transform ◽  
Geodesic Ray Transform

scholarly journals A Reflection Approach to the Broken Ray Transform

2015 ◽  
Vol 117 (2) ◽  
pp. 231 ◽  
Author(s):  
Joonas Ilmavirta
Keyword(s):  
Riemannian Manifolds ◽  
Ray Transform ◽  
Partial Data ◽  
Manifolds With Corners ◽  
Geodesic Ray Transform

We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity results for the broken ray transform using corresponding earlier results for the geodesic ray transform. Examples of manifolds where the broken ray transform is injective include Euclidean cones and parts of the spheres $S^n$. In addition, we introduce the periodic broken ray transform and use the reflection argument to produce examples of manifolds where it is injective. We also give counterexamples to both periodic and nonperiodic cases. The broken ray transform arises in Calderón's problem with partial data, and we give implications of our results for this application.

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