40 citations · 41 across the 5 of their papers we have counts for
5 papers
Non-standard Sobolev scales and the mapping properties of the X-ray transform on manifolds with strictly convex boundary
François Monard
This article surveys recent results aiming at obtaining refined mapping estimates for the X-ray transform on a Riemannian manifold with boundary, which leverage the condition that…
Inversion formulas and range characterizations for the attenuated geodesic ray transform
Yernat Assylbekov, François Monard, Gunther Uhlmann
We present two range characterizations for the attenuated geodesic X-ray transform defined on pairs of functions and one-forms on simple surfaces. Such characterizations are based…
Reconstruction of a fully anisotropic elasticity tensor from knowledge of displacement fields
Guillaume Bal, Francois Monard, Gunther Uhlmann
We present explicit reconstruction algorithms for fully anisotropic unknown elasticity tensors from knowledge of a finite number of internal displacement fields, with applications…
The geodesic ray transform on Riemannian surfaces with conjugate points
François Monard, Plamen Stefanov, Gunther Uhlmann
We study the geodesic X-ray transform on compact Riemannian surfaces with conjugate points. Regardless of the type of the conjugate points, we show that we cannot recover the s…
Imaging of anisotropic conductivities from current densities in two dimensions
Guillaume Bal, Chenxi Guo, François Monard
We consider the imaging of anisotropic conductivity tensors from knowledge of several internal current densities where sa…