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| Multi-parameter Tikhonov Regularization— An Augmented Approach |
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Citation： |
Kazufumi ITO,Bangti JIN,Tomoya TAKEUCHI.Multi-parameter Tikhonov Regularization— An Augmented Approach[J].Chinese Annals of Mathematics B,2014,35(3):383~398 |
| Page view： 2567
Net amount： 2092 |
Authors： |
Kazufumi ITO; Bangti JIN; Tomoya TAKEUCHI; |
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| 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 |
Classification： |
65J20, 65J22, 49N45 |
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