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Chinese Annals of Mathematics, Series B

, Volume 35, Issue 3, pp 383–398 | Cite as

Multi-parameter Tikhonov regularization — An augmented approach

  • Kazufumi ItoEmail author
  • Bangti Jin
  • Tomoya Takeuchi
Article

Abstract

We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.

Keywords

Multi-parameter regularization Augmented Tikhonov regularization, Balanced discrepancy principle 

2000 MR Subject Classification

65J20 65J22 49N45 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Center for Research in Scientific Computation & Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Department of MathematicsUniversity of California, RiversideRiversideUSA
  3. 3.Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial ScienceThe University of TokyoTokyoJapan

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