Iterated fractional Tikhonov regularization

作者：Bianchi Davide^*; Buccini Alessandro; Donatelli Marco; Serra Capizzano Stefano

来源：Inverse Problems, 2015, 31(5): 055005.

DOI：10.1088/0266-5611/31/5/055005

• Tikhonov regularization
• filter function
• iterated Tikhonov
• fractional Tikhonov
• weighted Tikhonov

Fractional Tikhonov regularization methods have been recently proposed to reduce the oversmoothing property of the Tikhonov regularization in standard form, in order to preserve the details of the approximated solution. Their regularization and convergence properties have been previously investigated showing that they are of optimal order. This paper provides saturation and converse results on their convergence rates. Using the same iterative refinement strategy of iterated Tikhonov regularization, new iterated fractional Tikhonov regularization methods are introduced. We show that these iterated methods are of optimal order and overcome the previous saturation results. Furthermore, nonstationary iterated fractional Tikhonov regularization methods are investigated, establishing their convergence rate under general conditions on the iteration parameters. Numerical results confirm the effectiveness of the proposed regularization iterations.

• 出版日期2015-5