Inverse problems with inexact forward operator: iterative regularization and application in dynamic imaging. (28th October 2020)

• Record Type: Journal Article
• Authors: Blanke, Stephanie E; Hahn, Bernadette N; Wald, Anne
• Is Part Of: Inverse problems. Volume 36:Number 12(2020)
• Publication Date: 2020-10-28
• Subjects: model inexactness -- dynamic computerized tomography -- sequential subspace optimization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abb5e1
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The classic regularization theory for solving inverse problems is built on the assumption that the forward operator perfectly represents the underlying physical model of the data acquisition. However, in many applications, for instance in microscopy or magnetic particle imaging, this is not the case. Another important example represent dynamic inverse problems, where changes of the searched-for quantity during data collection can be interpreted as model uncertainties. In this article, we propose a regularization strategy for linear inverse problems with inexact forward operator based on sequential subspace optimization methods (SESOP). In order to account for local modelling errors, we suggest to combine SESOP with the Kaczmarz' method. We study convergence and regularization properties of the proposed method and discuss several practical realizations. Relevance and performance of our approach are evaluated at simulated data from dynamic computerized tomography with various dynamic scenarios.