Variational Methods for Tomographic Reconstruction with Few Views

Maïtine Bergounioux; Isabelle Abraham; Romain Abraham; Guillaume Carlier; Erwan Le Pennec; Emmanuel Trélat

doi:10.1007/s00032-018-0285-1

Variational Methods for Tomographic Reconstruction with Few Views

Maïtine Bergounioux
, Isabelle Abraham
, Romain Abraham
, Guillaume Carlier
, Erwan Le Pennec
, Emmanuel Trélat

conventionnée avec l'Université d'Orléans
Centre d'Etudes de Limeil-Valenton
Université Paris Dauphine
Université Paris-Saclay
UPMC Université de Paris VI

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We deal with a severe ill posed problem, namely the reconstruction process of an image during tomography acquisition with (very) few views. We present different methods that we have been investigated during the past decade. They are based on variational analysis. This is a survey paper and we refer to the quoted papers for more details.

langue originale	Anglais
Pages (de - à)	157-200
Nombre de pages	44
journal	Milan Journal of Mathematics
Volume	86
Numéro de publication	2
Les DOIs	https://doi.org/10.1007/s00032-018-0285-1
état	Publié - 1 déc. 2018
Modification externe	Oui

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10.1007/s00032-018-0285-1

Contient cette citation

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title = "Variational Methods for Tomographic Reconstruction with Few Views",

abstract = "We deal with a severe ill posed problem, namely the reconstruction process of an image during tomography acquisition with (very) few views. We present different methods that we have been investigated during the past decade. They are based on variational analysis. This is a survey paper and we refer to the quoted papers for more details.",

keywords = "Radon operator, Tomographic reconstruction, fractional order Hilbert spaces, inverse problem, needlets, optimal transport, variational method",

author = "Ma{\"i}tine Bergounioux and Isabelle Abraham and Romain Abraham and Guillaume Carlier and \{Le Pennec\}, Erwan and Emmanuel Tr{\'e}lat",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature Switzerland AG.",

year = "2018",

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doi = "10.1007/s00032-018-0285-1",

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AU - Bergounioux, Maïtine

AU - Abraham, Isabelle

AU - Abraham, Romain

AU - Carlier, Guillaume

AU - Le Pennec, Erwan

AU - Trélat, Emmanuel

PY - 2018/12/1

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N2 - We deal with a severe ill posed problem, namely the reconstruction process of an image during tomography acquisition with (very) few views. We present different methods that we have been investigated during the past decade. They are based on variational analysis. This is a survey paper and we refer to the quoted papers for more details.

AB - We deal with a severe ill posed problem, namely the reconstruction process of an image during tomography acquisition with (very) few views. We present different methods that we have been investigated during the past decade. They are based on variational analysis. This is a survey paper and we refer to the quoted papers for more details.

KW - Radon operator

KW - Tomographic reconstruction

KW - fractional order Hilbert spaces

KW - inverse problem

KW - needlets

KW - optimal transport

KW - variational method

U2 - 10.1007/s00032-018-0285-1

DO - 10.1007/s00032-018-0285-1

M3 - Article

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VL - 86

SP - 157

EP - 200

JO - Milan Journal of Mathematics

JF - Milan Journal of Mathematics

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Variational Methods for Tomographic Reconstruction with Few Views

Résumé

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