The inverse problem of magnetorelaxometry imaging. (12th September 2018)

• Record Type: Journal Article
• Authors: Föcke, Janic; Baumgarten, Daniel; Burger, Martin
• Is Part Of: Inverse problems. Volume 34:Number 11(2018:Nov.)
• Publication Date: 2018-09-12
• Subjects: inverse source problem -- magnetorelaxometry imaging -- magnetic nanoparticles -- total variation regularization -- uniqueness -- magnetic remanence -- ADMM; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aadbbf
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The aim of this paper is to provide a solid mathematical discussion of the inverse problem in magnetorelaxometry imaging (MRXI), a currently developed technique for quantitative biomedical imaging using magnetic nanoparticles. We provide a detailed discussion of the mathematical modeling of the forward problems including possible ways to magnetically activate the particles and measure its magnetic response, leading to a severely ill-posed linear inverse problem. Moreover, we formulate an idealized version of the inverse problem for infinitesimal small activation coils, which allows for a more detailed analysis of uniqueness issues. We propose a variational regularization approach to compute stable approximations of the solution and discuss its discretization and numerical solution. Results on synthetic data are presented and improvements to methods used previously in practice are demonstrated.