Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule. (22nd January 2018)

• Record Type: Journal Article
• Authors: Jin, Qinian; Wang, Wei
• Is Part Of: Inverse problems. Volume 34:Number 3(2018:Mar.)
• Publication Date: 2018-01-22
• Subjects: nonlinear inverse problems -- the iteratively regularized Gauss–Newton method -- heuristic selection rule -- a posteriori error estimates -- convergence; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaa0fb
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.