The attenuated ray transform on simple surfaces
By Mikko Salo, Gunther Uhlmann. 2010
86 citations recorded by the source corpus.
We show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective. Moreover we give a stability estimate and develop a reconstruction procedure.
Subfields: Computer Vision and Pattern Recognition, Mathematical Physics, Media Technology
View Paper: https://www.semanticscholar.org/paper/2b0d451e35f001e7075963a4e1f8df0cefba36ff
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Vision and Pattern Recognition
- David dos Santos Ferreira
- Matti Lassas
- Mikko Salo
- Yaroslav Kurylev
- Gunther Uhlmann
- Richard Nickl
- Adam D. Bull
- D. Chetverikov
In Mathematical Physics
- Gunther Uhlmann
- Mikko Salo
- Matti Lassas
- David dos Santos Ferreira
- Yaroslav Kurylev
- Gabriel P. Paternain
- Richard Nickl
- F. Monard
In Media Technology
Citations in the corpus
- Statistical guarantees for Bayesian uncertainty quantification in nonlinear inverse problems with Gaussian process priors (2020, background): “These attenuated X-ray transforms are now well-studied [17, 46, 47, 48, 40, 57], and their connection to the scattering map (13) is as follows: the linearization of the map (13) about a point Φ involves an attenuated X-ray transform whose integrands belong to C∞(M,Cn×n), with attenuation Θ(Φ,Φ), a m”
- The Calderón problem in transversally anisotropic geometries (2013, methodology): “Instead of using injectivity for the attenuated ray transform (see [8, Section 7] and [36] for injectivity results), we will reduce matters to the unattenuated ray transform.”
- Invariant distributions, Beurling transforms and tensor tomography in higher dimensions (2014, background): “This interplay has lead to the solution of several long-standing geometric inverse problems, especially in two dimensions [19,20,37,38,41,44,51].”