Adaptive Regularization for Image Reconstruction from Subsampled Data

  • Michael HintermüllerEmail author
  • Andreas Langer
  • Carlos N. Rautenberg
  • Tao Wu
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


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.



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.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Michael Hintermüller
    • 1
    Email author
  • Andreas Langer
    • 2
  • Carlos N. Rautenberg
    • 3
  • Tao Wu
    • 4
  1. 1.Weierstrass InstituteBerlinGermany
  2. 2.Universität StuttgartStuttgartGermany
  3. 3.Humboldt-Universität zu BerlinBerlinGermany
  4. 4.Technische Universität MünchenGarchingGermany

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