Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme

A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers [Formula: see text] and [Formula: see text] . Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging...

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Detalles Bibliográficos
Autores principales: Davoli, Elisa, Fonseca, Irene, Liu, Pan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9984542/
https://www.ncbi.nlm.nih.gov/pubmed/36883103
http://dx.doi.org/10.1007/s00332-023-09902-4
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author Davoli, Elisa
Fonseca, Irene
Liu, Pan
author_facet Davoli, Elisa
Fonseca, Irene
Liu, Pan
author_sort Davoli, Elisa
collection PubMed
description A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers [Formula: see text] and [Formula: see text] . Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging data is proved by [Formula: see text] -convergence under a conditional uniform bound on the trace constant of the operators and a finite-null-space condition. Some first examples and numerical results are given.
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spelling pubmed-99845422023-03-05 Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme Davoli, Elisa Fonseca, Irene Liu, Pan J Nonlinear Sci Article A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers [Formula: see text] and [Formula: see text] . Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging data is proved by [Formula: see text] -convergence under a conditional uniform bound on the trace constant of the operators and a finite-null-space condition. Some first examples and numerical results are given. Springer US 2023-03-03 2023 /pmc/articles/PMC9984542/ /pubmed/36883103 http://dx.doi.org/10.1007/s00332-023-09902-4 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Davoli, Elisa
Fonseca, Irene
Liu, Pan
Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme
title Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme
title_full Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme
title_fullStr Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme
title_full_unstemmed Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme
title_short Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme
title_sort adaptive image processing: first order pde constraint regularizers and a bilevel training scheme
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9984542/
https://www.ncbi.nlm.nih.gov/pubmed/36883103
http://dx.doi.org/10.1007/s00332-023-09902-4
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AT fonsecairene adaptiveimageprocessingfirstorderpdeconstraintregularizersandabileveltrainingscheme
AT liupan adaptiveimageprocessingfirstorderpdeconstraintregularizersandabileveltrainingscheme

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