arXiv subjects

Lea Föcke

Publications and source records attributed to Lea Föcke.

3 recordsLinked to original sources

arXiv2021

SiMRX -- A Simulation toolbox for MRX

SiMRX is a MRX simulation toolbox written in MATLAB for simulation of realistic 2D and 3D Magnetorelaxometry (MRX) setups, including coils, sensors and activation patterns. MRX is a new modality that uses magnetic nanoparticles (MNP) as contrast agent and shows promising results in medical applications, e.g. cancer treatment. Its basic principles were outlined in [Baumgarten et al., 2008], further elaborated in [Liebl et al., 2014], transferred into a rigorous mathematical model and analyzed in [Föcke et al., 2018]. SiMRX is available at https://gitlab.com/simrx/simrx/.

cs.CE↗

arXiv2021

Reconstruction Methods in THz Single-pixel Imaging

The aim of this paper is to discuss some advanced aspects of image reconstruction in single-pixel cameras, focusing in particular on detectors in the THz regime. We discuss the reconstruction problem from a computational imaging perspective and provide a comparison of the effects of several state-of-the art regularization techniques. Moreover, we focus on some advanced aspects arising in practice with THz cameras, which lead to nonlinear reconstruction problems: the calibration of the beam reminiscent of the Retinex problem in imaging and phase recovery problems. Finally we provide an outlook to future challenges in the area.

math.OC↗

arXiv2021

The Inverse Problem of Magnetorelaxometry Imaging

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 activate and measure, 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 are presented and improvements to methods used previously in practice are demonstrated. Finally we give an outlook to further questions and in particular experimental design.

math.NA↗