Adaptive Regularization for Image Reconstruction from Subsampled Data

Michael Hintermüller; Andreas Langer; Carlos N. Rautenberg; Tao Wu

doi:10.1007/978-3-319-91274-5_1

Adaptive Regularization for Image Reconstruction from Subsampled Data

Michael Hintermüller, Andreas Langer, Carlos N. Rautenberg, Tao Wu

Forskningsoutput: Kapitel i bok/rapport/Conference proceeding › Konferenspaper i proceeding › Peer review

Sammanfattning

Choices of regularization parameters are central to variational methods for image restoration. In this paper, a spatially adaptive (or distributed) regularization scheme is developed based on localized residuals, which properly balances the regularization weight between regions containing image details and homogeneous regions. Surrogate iterative methods are employed to handle given subsampled data in transformed domains, such as Fourier or wavelet data. In this respect, this work extends the spatially variant regularization technique previously established in Dong et al. (J Math Imaging Vis 40:82–104, 2011), which depends on the fact that the given data are degraded images only. Numerical experiments for the reconstruction from partial Fourier data and for wavelet inpainting prove the efficiency of the newly proposed approach.

Originalspråk	engelska
Titel på värdpublikation	Proceedings of the International Conference on Imaging, Vision and Learning Based Optimization and PDEs. ILVOPDE 2016.
Sidor	3-26
Antal sidor	24
Volym	0
Utgåva	221219
DOI	https://doi.org/10.1007/978-3-319-91274-5_1
Status	Published - 2018
Externt publicerad	Ja
Evenemang	International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016 - Bergen, Norge Varaktighet: 2016 aug. 29 → 2016 sep. 2

Publikationsserier

Namn	Mathematics and Visualization
ISSN (tryckt)	1612-3786

Konferens

Konferens	International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016
Land/Territorium	Norge
Ort	Bergen
Period	2016/08/29 → 2016/09/02

Bibliografisk information

Funding Information:
Acknowledgements This research was supported by the Austrian Science Fund (FWF) through START-Project Y305 “Interfaces and Free Boundaries” and SFB-Project F3204 “Mathematical Optimization and Applications in Biomedical Sciences”, the German Research Foundation DFG through Project HI1466/7-1 “Free Boundary Problems and Level Set Methods”, as well as the Research Center MATHEON through Project C-SE15 “Optimal Network Sensor Placement for Energy Efficiency” supported by the Einstein Center for Mathematics Berlin.

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

Ämnesklassifikation (UKÄ)

Matematisk analys
Datorgrafik och datorseende

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10.1007/978-3-319-91274-5_1

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title = "Adaptive Regularization for Image Reconstruction from Subsampled Data",

abstract = "Choices of regularization parameters are central to variational methods for image restoration. In this paper, a spatially adaptive (or distributed) regularization scheme is developed based on localized residuals, which properly balances the regularization weight between regions containing image details and homogeneous regions. Surrogate iterative methods are employed to handle given subsampled data in transformed domains, such as Fourier or wavelet data. In this respect, this work extends the spatially variant regularization technique previously established in Dong et al. (J Math Imaging Vis 40:82–104, 2011), which depends on the fact that the given data are degraded images only. Numerical experiments for the reconstruction from partial Fourier data and for wavelet inpainting prove the efficiency of the newly proposed approach.",

author = "Michael Hinterm{\"u}ller and Andreas Langer and Rautenberg, {Carlos N.} and Tao Wu",

note = "Funding Information: Acknowledgements This research was supported by the Austrian Science Fund (FWF) through START-Project Y305 “Interfaces and Free Boundaries” and SFB-Project F3204 “Mathematical Optimization and Applications in Biomedical Sciences”, the German Research Foundation DFG through Project HI1466/7-1 “Free Boundary Problems and Level Set Methods”, as well as the Research Center MATHEON through Project C-SE15 “Optimal Network Sensor Placement for Energy Efficiency” supported by the Einstein Center for Mathematics Berlin. Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.; International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016 ; Conference date: 29-08-2016 Through 02-09-2016",

year = "2018",

doi = "10.1007/978-3-319-91274-5_1",

language = "English",

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Hintermüller, M, Langer, A, Rautenberg, CN & Wu, T 2018, Adaptive Regularization for Image Reconstruction from Subsampled Data. i Proceedings of the International Conference on Imaging, Vision and Learning Based Optimization and PDEs. ILVOPDE 2016.. 221219 uppl, vol. 0, Mathematics and Visualization, s. 3-26, International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016, Bergen, Norge, 2016/08/29. https://doi.org/10.1007/978-3-319-91274-5_1

Adaptive Regularization for Image Reconstruction from Subsampled Data. / Hintermüller, Michael; Langer, Andreas; Rautenberg, Carlos N. et al.
Proceedings of the International Conference on Imaging, Vision and Learning Based Optimization and PDEs. ILVOPDE 2016.. Vol. 0 221219. uppl. 2018. s. 3-26 (Mathematics and Visualization).

Forskningsoutput: Kapitel i bok/rapport/Conference proceeding › Konferenspaper i proceeding › Peer review

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N1 - Funding Information: Acknowledgements This research was supported by the Austrian Science Fund (FWF) through START-Project Y305 “Interfaces and Free Boundaries” and SFB-Project F3204 “Mathematical Optimization and Applications in Biomedical Sciences”, the German Research Foundation DFG through Project HI1466/7-1 “Free Boundary Problems and Level Set Methods”, as well as the Research Center MATHEON through Project C-SE15 “Optimal Network Sensor Placement for Energy Efficiency” supported by the Einstein Center for Mathematics Berlin. Publisher Copyright: © 2018, Springer International Publishing AG, part of Springer Nature. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

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AB - Choices of regularization parameters are central to variational methods for image restoration. In this paper, a spatially adaptive (or distributed) regularization scheme is developed based on localized residuals, which properly balances the regularization weight between regions containing image details and homogeneous regions. Surrogate iterative methods are employed to handle given subsampled data in transformed domains, such as Fourier or wavelet data. In this respect, this work extends the spatially variant regularization technique previously established in Dong et al. (J Math Imaging Vis 40:82–104, 2011), which depends on the fact that the given data are degraded images only. Numerical experiments for the reconstruction from partial Fourier data and for wavelet inpainting prove the efficiency of the newly proposed approach.

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Adaptive Regularization for Image Reconstruction from Subsampled Data

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