Inverse Problem Analysis in Magnetic Nanoparticle Tomography Using Minimum Variance Spatial Filter

Abstract

In magnetic nanoparticle tomography (MNT), the reduction of artifacts and the calculation time can be used to estimate the position of magnetic nanoparticles (MNPs). A non-negative least-squares (NNLS) inverse problem analysis has been used in MNT systems for this task. However, due to the presence of measurement noise and the high sensitivity of the NNLS method, it often estimates certain MNPs inaccurately, i.e., it generates artifacts. In addition, its calculation time is very high. In this study, we applied the minimum variance spatial filter (MV-SF) inverse problem analysis to MNT and estimated the position of an MNP sample containing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100~\mu \text{g}$ </tex-math></inline-formula> of Fe. Using the MV-SF method, MNP samples placed at a depth of 25–40 mm were observed to have no artifacts. Moreover, the MV-SF method was also observed to be faster than the NNLS method by a factor of approximately 20. These results verify the feasibility of the MV-SF method for estimating the MNP positions in an MNT system.