Multi-parameter Tikhonov regularization — An augmented approach

• DOI: 10.1007/s11401-014-0835-y
• Publication Date: 2014-05-03T16:47:20Z
• Authors: Kazufumi Ito; Bangti Jin; Tomoya Takeuchi
• Keywords: Regularization; Deblurring; Backus–Gilbert method

14 pages, to appear in Chinese Annals of Mathematics, Series B, special issue for International Conference on Inverse Problems and Related Topics<br/>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 \textit{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 denoising are presented to illustrate the feasibility of the balanced discrepancy principle.<br/>