44 citations · 182 across the 18 of their papers we have counts for
26 papers
Supercritical magnetic ray transforms in hyperbolic space: the complexification method from the transport-twistor lens
François Monard
We present new inversion formulas for the unattenuated and attenuated magnetic ray transforms in the Poincaré disk, in the case of a constant, supercritical magnetic field. Our app…
Singularly Weighted X-ray Tensor Tomography
Jonathan Kay, François Monard
If is a boundary defining function for the Euclidean unit disk and denotes the geodesic X-ray transform, for , we study the singularly-weighted X-ray transform…
Tensor Tomography on Asymptotically Hyperbolic Surfaces
Nikolas Eptaminitakis, François Monard, Yuzhou Joey Zou
We initiate a study of the inversion of the geodesic X-ray transform over symmetric -tensor fields on asymptotically hyperbolic surfaces. This operator has a non-trivial k…
Biholomorphism Rigidity for Transport Twistor Spaces
Jan Bohr, François Monard, Gabriel P. Paternain
We prove that biholomorphisms between the transport twistor spaces of simple or Anosov surfaces exhibit rigidity: they must be, up to constant rescaling and the antipodal map, the…
The -isomorphism property for a class of singularly-weighted X-ray transforms
Rohit Kumar Mishra, François Monard, Yuzhou Zou
We study a one-parameter family of self-adjoint normal operators for the X-ray transform on the closed Euclidean disk , obtained by considering specific singularly wei…
Sampling the X-ray transform on simple surfaces
François Monard, Plamen Stefanov
We study the problem of proper discretizing and sampling issues related to geodesic X-ray transforms on simple surfaces, and illustrate the theory on simple geodesic disks of const…
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…
Imaging of isotropic and anisotropic conductivities from power densities in three dimensions
François Monard, Donsub Rim
We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises…
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…
The geodesic X-ray transform with a -connection
François Monard, Gabriel P. Paternain
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all tran…
Efficient tensor tomography in fan-beam coordinates
Francois Monard
We propose a thorough analysis of the tensor tomography problem on the Euclidean unit disk parameterized in fan-beam coordinates. This includes, for the inversion of the Radon tran…
Inversion of the attenuated geodesic X-ray transform over functions and vector fields on simple surfaces
François Monard
We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of si…
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…
On reconstruction formulas for the ray transform acting on symmetric differentials on surfaces
François Monard
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and…
Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements
Guillaume Bal, Cédric Bellis, Sébastien Imperiale +1
Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim…
Numerical implementation of geodesic X-ray transforms and their inversion
François Monard
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each…
Inverse anisotropic conductivity from internal current densities
Guillaume Bal, Chenxi Guo, Francois Monard
This paper concerns the reconstruction of an anisotropic conductivity tensor from internal current densities of the form , where solves a second-order ellipt…
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…
Inverse transport with isotropic time-harmonic sources
Guillaume Bal, Francois Monard
This paper concerns the reconstruction of the scattering coefficient in a two-dimensional transport equation from angularly averaged measurements when the probing source is isotrop…
Inverse anisotropic diffusion from power density measurements in two dimensions
Francois Monard, Guillaume Bal
This paper concerns the reconstruction of an anisotropic diffusion tensor from knowledge of internal functionals of the form $γ\nabla u_i\cdot\nabla…