Journal
INVERSE PROBLEMS
Volume 34, Issue 3, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6420/aaa0fb
Keywords
nonlinear inverse problems; the iteratively regularized Gauss-Newton method; heuristic selection rule; a posteriori error estimates; convergence
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Funding
- Future Fellowship of the Australian Research Council
- National Natural Science Foundation of China [11401257]
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The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.
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