Automated Parameter Selection for Total Variation Minimization in Image Restoration

A. Langer

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an Lτ-data fidelity term, τ∈{1,2}, are presented. The automated selection of the regularization parameter is based on the discrepancy principle, whereby in each iteration a total variation model has to be minimized. In the case of a locally varying parameter, this amounts to solve a multiscale total variation minimization problem. For solving the constituted multiscale total variation model, convergent first- and second-order methods are introduced and analyzed. Numerical experiments for image denoising and image deblurring show the efficiency, the competitiveness, and the performance of the proposed fully automated scalar and locally varying parameter selection algorithms.
Original languageEnglish
Pages (from-to)239–268
Number of pages30
JournalJournal of Mathematical Imaging and Vision
Early online date22 Jul 2016
Publication statusPublished - 2017
Externally publishedYes


  • Locally dependent regularization parameter
  • Automated parameter selection
  • Discrepancy principle
  • Constrained/unconstrained problem
  • Gaussian noise
  • Impulse noise


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