Robustness Assessment of 1-D Electron Paramagnetic Resonance for Improved Magnetic Nanoparticle Reconstructions

Electron paramagnetic resonance (EPR) is a sensitive measurement technique which can be used to recover the 1-D spatial distribution of magnetic nanoparticles (MNP) noninvasively. This can be achieved by solving an inverse problem that requires a numerical model for interpreting the EPR measurement data. This paper assesses the robustness of this technique by including different types of errors such as setup errors, measurement errors, and sample positioning errors in the numerical model. The impact of each error is estimated for different spatial MNP distributions. Additionally, our error models are validated by comparing the simulated impact of errors to the impact on lab EPR measurements. Furthermore, we improve the solution of the inverse problem by introducing a combination of truncated singular value decomposition and nonnegative least squares. This combination enables to recover both smooth and discontinuous MNP distributions. From this analysis, conclusions are drawn to improve MNP reconstructions with EPR and to state requirements for using EPR as a 2-D and 3-D imaging technique for MNP.