11 citations · 11 across the 2 of their papers we have counts for
5 papers
Functional relations, sharp mapping properties and regularization of the X-ray transform on disks of constant curvature
François Monard
On simple geodesic disks of constant curvature, we derive new functional relations for the geodesic X-ray transform, involving a certain class of elliptic differential operators wh…
Consistent Inversion of Noisy Non-Abelian X-Ray Transforms
François Monard, Richard Nickl, Gabriel P. Paternain
For a simple surface, the non-linear statistical inverse problem of recovering a matrix field from discrete, noisy measurements of the -value…
The attenuated geodesic X-ray transform
Sean Holman, François Monard, Plamen Stefanov
This article deals with stability issues related to geodesic X-ray transforms, where an interplay between the (attenuation type) weight in the transform and the underlying geometry…
Linearized internal functionals for anisotropic conductivities
Guillaume Bal, Chenxi Guo, Francois Monard
This paper concerns the reconstruction of an anisotropic conductivity tensor in an elliptic second-order equation from knowledge of the so-called power density functionals. This pr…
Inverse anisotropic conductivity from power densities in dimension
Francois Monard, Guillaume Bal
We investigate the problem of reconstructing a fully anisotropic conductivity tensor from internal functionals of the form where solves $\nabla\cdo…