2019, Oelsner, Gregor, Schultze, Volkmar, Ijsselsteijn, Rob, Stolz, Ronny

We experimentally investigate the influence of the orientation of optically pumped magnetometers in Earth’s magnetic field. We focus our analysis to an operational mode that promises femtotesla field resolutions at such field strengths. For this so-called light-shift dispersed Mz (LSD-Mz) regime, we focus on the key parameters defining its performance. That are the reconstructed Larmor frequency, the transfer function between output signal and magnetic field amplitude as well as the shot noise limited field resolution. We demonstrate that due to the use of two well balanced laser beams for optical pumping with different helicities the heading error as well as the field sensitivity of a detector both are only weakly influenced by the heading in a large orientation angle range.

2018, Dong, Guozhi, Hintermüller, Michael, Papafitsoros, Kostas

Quantitative magnetic resonance imaging (qMRI) denotes the task of estimating the values of magnetic and tissue parameters, e.g., relaxation times T1, T2, proton density p and others. Recently in [Ma et al., Nature, 2013], an approach named Magnetic Resonance Fingerprinting (MRF) was introduced, being capable of simultaneously recovering these parameters by using a two step procedure: (i) a series of magnetization maps are created and then (ii) these are matched to parameters with the help of a pre-computed dictionary (Bloch manifold). In this paper, we initially put MRF and its variants in the perspective of optimization and inverse problems, providing some mathematical insights into these methods. Motivated by the fact that the Bloch manifold is non-convex, and the accuracy of the MRF type algorithms is limited by the discretization size of the dictionary, we propose here a novel physically oriented method for qMRI. In contrast to the conventional two step models, our model is dictionary-free and it is described by a single nonlinear equation, governed by an operator for which we prove differentiability and other properties. This non-linear equation is efficiently solved via robust Newton type methods. The effectiveness of our method for noisy and undersampled data is shown both analytically and via numerical examples where also improvement over MRF and its variants is observed.