Adaptive Regularization for Image Reconstruction from Subsampled Data

M. Hintermüller; A. Langer; C.N. Rautenberg; T. Wu

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

Adaptive Regularization for Image Reconstruction from Subsampled Data

M. Hintermüller, A. Langer, C.N. Rautenberg, T. Wu

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

3 Citations (Scopus)

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.

Original language	English
Title of host publication	Proceedings of the International Conference on Imaging, Vision and Learning Based Optimization and PDEs. ILVOPDE 2016
Publisher	Springer, Cham
Pages	3-26
Number of pages	24
ISBN (Electronic)	978-3-319-91274-5
ISBN (Print)	978-3-319-91273-8
DOIs	https://doi.org/10.1007/978-3-319-91274-5_1
Publication status	Published - 20 Nov 2018
Externally published	Yes
Event	International Conference on Imaging, Vision and Learning based on Optimization and PDEs - Bergen, Norway Duration: 29 Aug 2016 → 2 Sept 2016

Conference

Conference	International Conference on Imaging, Vision and Learning based on Optimization and PDEs
Abbreviated title	IVLOPDE 2016
Country/Territory	Norway
City	Bergen
Period	29/08/16 → 2/09/16

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

Cite this

Adaptive Regularization for Image Reconstruction from Subsampled Data. / Hintermüller, M.; Langer, A.; Rautenberg, C.N. et al.
Proceedings of the International Conference on Imaging, Vision and Learning Based Optimization and PDEs. ILVOPDE 2016. Springer, Cham , 2018. p. 3-26.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding › peer-review

Hintermüller, M, Langer, A, Rautenberg, CN & Wu, T 2018, Adaptive Regularization for Image Reconstruction from Subsampled Data. in Proceedings of the International Conference on Imaging, Vision and Learning Based Optimization and PDEs. ILVOPDE 2016. Springer, Cham , pp. 3-26, International Conference on Imaging, Vision and Learning based on Optimization and PDEs, Bergen, Norway, 29/08/16. https://doi.org/10.1007/978-3-319-91274-5_1

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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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