  Magnetic particle imaging is an emerging quantitative imaging modality,
exploiting the unique nonlinear magnetization phenomenon of superparamagnetic
iron oxide nanoparticles for recovering the concentration. Traditionally the
reconstruction is formulated into a penalized least-squares problem with
nonnegativity constraint, and then solved using a variant of Kaczmarz method
which is often stopped early after a small number of iterations. Besides the
phantom signal, measurements additionally include a background signal and a
noise signal. In order to obtain good reconstructions, a preprocessing step of
frequency selection to remove the deleterious influences of the noise is often
adopted. In this work, we propose a complementary pure variational approach to
noise treatment, by viewing highly noisy measurements as outliers, and
employing the l1 data fitting, one popular approach from robust statistics.
When compared with the standard approach, it is easy to implement with a
comparable computational complexity. Experiments with a public domain dataset,
i.e., Open MPI dataset, show that it can give accurate reconstructions, and is
less prone to noisy measurements, which is illustrated by quantitative (PSNR /
SSIM) and qualitative comparisons with the Kaczmarz method. We also investigate
the performance of the Kaczmarz method for small iteration numbers
quantitatively.
