WIAS Preprint No. 2379, (2017)

Adaptive regularization for image reconstruction from subsampled data


  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Langer, Andreas
  • Rautenberg, Carlos N.
  • Wu, Tao

2010 Mathematics Subject Classification

  • 68U10 94A08 49K20 49K40 49M37 47A52 65K10


  • image restoration, spatially adaptive regularization, partial Fourier data, wavelet inpainting




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 [15], 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.

Appeared in

  • Imaging, Vision and Learning Based on Optimization and PDEs IVLOPDE, Bergen, Norway, August 29 - September 2, 2016, X.-Ch. Tai, E. Bae, M. Lysaker, eds., Mathematics and Visualization, Springer International Publishing, Berlin, 2017, pp. Part 1, Chapter 1, DOI 10.1007/978-3-319-91274-5 .

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