A projective averaged Kaczmarz iteration for nonlinear ill-posed problems. (2nd September 2020)

• Record Type: Journal Article
• Authors: Tong, Shanshan; Han, Bo; Tang, Jinping
• Is Part Of: Inverse problems. Volume 36:Number 9(2020)
• Publication Date: 2020-09-02
• Subjects: nonlinear ill-posed problems -- iterative regularization method -- Kaczmarz method -- projective method -- homotopy perturbation Kaczmarz; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aba5ef
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The averaged Kaczmarz iteration is a hybrid of the Landweber method and Kaczmarz method with easy implementation and increased stability for solving problems with multi nonlinear equations. In this paper, we propose an accelerated averaged Kaczmarz type iterative method by introducing the search direction of homotopy perturbation Kaczmarz and a projective strategy. The new iterate is updated by using an average over the intermediate variables. These variables are obtained by the metric projection of previous iterates onto the stripes which are related to the property of forward operator and noise level. We present the convergence analysis of the proposed method under the similar assumptions of Landweber Kaczmarz method. The numerical experiments on parameter identification problem validate that the proposed method has evident acceleration effect and reconstruction stability.