A Convex Variational Model for Learning Convolutional Image Atoms from Incomplete Data.
Convex relaxation
Convolutional Lasso
Functional lifting
Inverse problems
Learning approaches
Machine learning
Texture reconstruction
Variational methods
Journal
Journal of mathematical imaging and vision
ISSN: 0924-9907
Titre abrégé: J Math Imaging Vis
Pays: Netherlands
ID NLM: 101512096
Informations de publication
Date de publication:
2020
2020
Historique:
received:
07
12
2018
accepted:
03
10
2019
entrez:
18
4
2020
pubmed:
18
4
2020
medline:
18
4
2020
Statut:
ppublish
Résumé
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is convex and allows for simultaneous image reconstruction and atom learning in a general, inverse problems context. Further, motivated by an improved numerical performance, also a semi-convex variant is included in the analysis and the experiments of the paper. For both settings, fundamental analytical properties allowing in particular to ensure well-posedness and stability results for inverse problems are proven in a continuous setting. Exploiting convexity, globally optimal solutions are further computed numerically for applications with incomplete, noisy and blurry data and numerical results are shown.
Identifiants
pubmed: 32300265
doi: 10.1007/s10851-019-00919-7
pii: 919
pmc: PMC7138786
doi:
Types de publication
Journal Article
Langues
eng
Pagination
417-444Informations de copyright
© The Author(s) 2019.
Références
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