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.
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This work was supported by the Army Research Office under DAAD19-02-1-0394, US-ARO grant 49308-MA, and US-AFSOR grant FA9550-06-1-0241.
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Ito, K., Jin, B. & Takeuchi, T. Multi-parameter Tikhonov regularization — An augmented approach. Chin. Ann. Math. Ser. B 35, 383–398 (2014). https://doi.org/10.1007/s11401-014-0835-y
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DOI: https://doi.org/10.1007/s11401-014-0835-y