Multi-parameter Tikhonov regularization — An augmented approach
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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.
KeywordsMulti-parameter regularization Augmented Tikhonov regularization, Balanced discrepancy principle
2000 MR Subject Classification65J20 65J22 49N45
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