A Spatio-Temporal Approach for the Solution of the Inverse Problem in the Reconstruction of Magnetic Nanoparticle Distributions

The estimation of magnetic nanoparticle distributions is essential for their medical application. A possible technique is the reconstruction of these distributions from multichannel magnetorelaxometry measurements. In this paper, a novel minimum norm approach for the solution of this inverse problem based on a spatio-temporal expansion of the generally applied spatial lead field matrix is presented. The performance of this method is quantitatively studied in simulations and compared to the conventional static technique. The influence of the relevant parameters signal-to-noise ratio in the data, time constant of the temporal model, and TSVD regularization parameter is investigated. Our results indicate that the novel spatio-temporal approach significantly improves the reconstruction quality.