Variational Methods for Tomographic Reconstruction with Few Views

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...

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Bibliographic Details
Published inMilan journal of mathematics Vol. 86; no. 2; pp. 157 - 200
Main Authors Bergounioux, Maïtine, Abraham, Isabelle, Abraham, Romain, Carlier, Guillaume, Le Pennec, Erwan, Trélat, Emmanuel
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2018
Springer Verlag
Subjects
Analysis
Mathematics
Mathematics and Statistics
Optimization and Control
fractional order Hilbert spaces
inverse problem
45Q05
Radon operator
49K40
variational method
optimal transport
needlets
Tomographic reconstruction
65M32
Needlets
Spaces
Fractional order Hilbert
Variational method
transport
Optimal
Inverse problem
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Summary: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.
ISSN:1424-9286
1424-9294
DOI:10.1007/s00032-018-0285-1