Adaptive Regularization for Image Reconstruction from Subsampled Data
(2018) International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016 In Mathematics and Visualization p.3-26- 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... (More)
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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- author
- Hintermüller, Michael ; Langer, Andreas LU ; Rautenberg, Carlos N. and Wu, Tao
- publishing date
- 2018
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the International Conference on Imaging, Vision and Learning Based Optimization and PDEs. ILVOPDE 2016.
- series title
- Mathematics and Visualization
- edition
- 221219
- pages
- 24 pages
- conference name
- International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016
- conference location
- Bergen, Norway
- conference dates
- 2016-08-29 - 2016-09-02
- external identifiers
-
- scopus:85057465908
- ISSN
- 1612-3786
- DOI
- 10.1007/978-3-319-91274-5_1
- language
- English
- LU publication?
- no
- additional info
- 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.
- id
- 3cb0c1e0-df34-4f39-a4cb-a51d372c4599
- date added to LUP
- 2021-03-15 22:29:43
- date last changed
- 2022-04-03 17:05:39
@inproceedings{3cb0c1e0-df34-4f39-a4cb-a51d372c4599,
abstract = {{<p>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.</p>}},
author = {{Hintermüller, Michael and Langer, Andreas and Rautenberg, Carlos N. and Wu, Tao}},
booktitle = {{Proceedings of the International Conference on Imaging, Vision and Learning Based Optimization and PDEs. ILVOPDE 2016.}},
issn = {{1612-3786}},
language = {{eng}},
pages = {{3--26}},
series = {{Mathematics and Visualization}},
title = {{Adaptive Regularization for Image Reconstruction from Subsampled Data}},
url = {{http://dx.doi.org/10.1007/978-3-319-91274-5_1}},
doi = {{10.1007/978-3-319-91274-5_1}},
year = {{2018}},
}