The X-Ray Transform for a Generic Family of Curves and Weights
By Andrew Béla Frigyik, Plamen Stefanov, Gunther Uhlmann. 2007
121 citations recorded by the source corpus.
Abstract We study the weighted integral transform on a compact manifold with boundary over a smooth family of curves Γ. We prove generic injectivity and a stability estimate under the condition that the conormal bundle of Γ covers T*M.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3d02a93a9fdd7017b7d0ea22b8fbefb48fbcdeef
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In Computational Theory and Mathematics
- Gunther Uhlmann
- Mikko Salo
- Plamen Stefanov
- Guillaume Bal
- Katya Krupchyk
- Venkateswaran P. Krishnan
- Matti Lassas
- András Vasy
In Mathematical Physics
- Gunther Uhlmann
- Mikko Salo
- Guillaume Bal
- Plamen Stefanov
- Matti Lassas
- Katya Krupchyk
- Yi-Hsuan Lin
- David dos Santos Ferreira
Citations in the corpus
- The geodesic X-ray transform with fold caustics (2010, methodology): “for all k ≥ 0; see [Stefanov and Uhlmann 2004; Frigyik et al. 2008], and [Stefanov and Uhlmann 2008] for a class of manifolds with conjugate points.”
- Sensitivity analysis of an inverse problem for the wave equation with caustics (2012, unknown): “Then “fold-regular metric” generalizes “regular metric” introduced in [29].”
- A Support Theorem for the Geodesic Ray Transform on Functions (2007, unknown): “We also mention a recent work of Frigyik-Stefanov-Uhlmann in [5] where similar ideas based on the complex stationary phase method are used.”
- The attenuated ray transform on simple surfaces (2010, background): “A similar result, with a slightly different smallness condition, also follows from the general stability theory of [10].”
- Inverse transport theory and applications (2009, methodology): “Moreover, the regularization properties of L ,w are established in [56].”