Zobrazeno 1 - 10
of 38
pro vyhledávání: '"François Monard"'
Autor:
Rohit Mishra, François Monard
Publikováno v:
Journal of Spectral Theory. 11:1005-1041
For a one-parameter family of simple metrics of constant curvature ($4\kappa$ for $\kappa\in (-1,1)$) on the unit disk $M$, we first make explicit the Pestov-Uhlmann range characterization of the geodesic X-ray transform, by constructing a basis of f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ce3fbe0e897fc2cb7d2cffbf5012a6c1
https://doi.org/10.4171/jst/364
https://doi.org/10.4171/jst/364
We study a one-parameter family of self-adjoint normal operators for the X-ray transform on the closed Euclidean disk ${\mathbb D}$, obtained by considering specific singularly weighted $L^2$ topologies. We first recover the well-known Singular Value
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c21090917f07549020c101c14846d52b
http://arxiv.org/abs/2203.09861
http://arxiv.org/abs/2203.09861
Publikováno v:
Communications on Pure and Applied Mathematics
For $M$ a simple surface, the non-linear statistical inverse problem of recovering a matrix field $\Phi: M \to \mathfrak{so}(n)$ from discrete, noisy measurements of the $SO(n)$-valued scattering data $C_\Phi$ of a solution of a matrix ODE is conside
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04f69aade0b00392ca52dd82f78351dd
https://doi.org/10.1002/cpa.21942
https://doi.org/10.1002/cpa.21942
Publikováno v:
Journal of Inverse and Ill-posed Problems. 27:527-538
We first give a constructive answer to the attenuated tensor tomography problem on simple surfaces. We then use this result to propose two approaches to produce vector-valued integral transforms which are fully injective over tensor fields. The first
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d543f3f073b879401471e7bd8aca7516
https://doi.org/10.1515/jiip-2018-0067
https://doi.org/10.1515/jiip-2018-0067
Publikováno v:
Journal de Mathématiques Pures et Appliquées. 111:161-190
We present two range characterizations for the attenuated geodesic X-ray transform defined on pairs of functions and 1-forms on simple surfaces. Such characterizations are based on first isolating the range over sums of functions and 1-forms, then se
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::712aa2b5d774ffcdec201ef0268eba84
https://doi.org/10.1016/j.matpur.2017.09.006
https://doi.org/10.1016/j.matpur.2017.09.006
Autor:
François Monard
Publikováno v:
Inverse Problems & Imaging. 12:433-460
This article extends the author's past work [ 11 ] to attenuated X-ray transforms, where the attenuation is complex-valued and only depends on position. We give a positive and constructive answer to the attenuated tensor tomography problem on the Euc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::72c4a17fec3715e8f4aca65684808468
https://doi.org/10.3934/ipi.2018019
https://doi.org/10.3934/ipi.2018019
Autor:
Gabriel P. Paternain, François Monard
Publikováno v:
The Journal of Geometric Analysis. 30:2515-2557
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of all such transforms in a neighborhood of constant curvature metrics and non-unitary
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7e4bf681c0066ee84e1ff38191d5e4f3
https://doi.org/10.1007/s12220-017-9931-z
https://doi.org/10.1007/s12220-017-9931-z
Autor:
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 whose ellipticity degenerates normally at the boundary. We then use thes
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::063ead6b0fd6f154d790bfccf1380837
Publikováno v:
Ann. Statist. 47, no. 2 (2019), 1113-1147
The Annals of Statistics
The Annals of Statistics
We consider the statistical inverse problem of recovering a function $f: M \to \mathbb R$, where $M$ is a smooth compact Riemannian manifold with boundary, from measurements of general $X$-ray transforms $I_a(f)$ of $f$, corrupted by additive Gaussia
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ba8cac256deaa4007508b8a13d42a91
http://arxiv.org/abs/1708.06332
http://arxiv.org/abs/1708.06332
Autor:
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 in the coupled-physics imaging modality Ultrasound Modulated Electrica
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f4b64b92f74dc2bdd58c816db4a30a9