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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	157-200
Number of pages	44
Journal	Milan Journal of Mathematics
Volume	86
Issue number	2
DOIs	https://doi.org/10.1007/s00032-018-0285-1
Publication status	Published - 1 Dec 2018
Externally published	Yes

Keywords

Radon operator
Tomographic reconstruction
fractional order Hilbert spaces
inverse problem
needlets
optimal transport
variational method

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10.1007/s00032-018-0285-1

Cite this

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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",

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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.

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KW - Radon operator

KW - Tomographic reconstruction

KW - fractional order Hilbert spaces

KW - inverse problem

KW - needlets

KW - optimal transport

KW - variational method

UR - https://www.scopus.com/pages/publications/85053795396

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JO - Milan Journal of Mathematics

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Variational Methods for Tomographic Reconstruction with Few Views

Abstract

Keywords

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