An iterative regularization method for nonlinear problems based on Bregman projections. (3rd October 2016)

• Record Type: Journal Article
• Authors: Maaß, Peter; Strehlow, Robin
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-10-03
• Subjects: regularization -- Bregman projection -- nonlinear operator -- iterative regularization method -- inverse problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115013
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we present an iterative method for the regularization of ill-posed, nonlinear problems. The approach is based on the Bregman projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. In our investigations, we follow (Lorenz et al 2014 SIAM J. Imaging Sci. 7 1237–62 ) and extend the respective method to the setting of nonlinear operators. Furthermore, we present a proof for the regularizing properties of the method.