Deep Learning for Restoring MPI System Matrices Using Simulated Training Data

Abstract

Magnetic particle imaging reconstructs tracer distributions using a system matrix obtained through time-consuming, noise-prone calibration measurements. Methods for addressing imperfections in measured system matrices increasingly rely on deep neural networks, yet curated training data remain scarce. This study evaluates whether physics-based simulated system matrices can be used to train deep learning models for different system matrix restoration tasks, i.e., denoising, accelerated calibration, upsampling, and inpainting, that generalize to measured data. A large system matrices dataset was generated using an equilibrium magnetization model extended with uniaxial anisotropy. The dataset spans particle, scanner, and calibration parameters for 2D and 3D trajectories, and includes background noise injected from empty-frame measurements. For each restoration task, deep learning models were compared with classical non-learning baseline methods. The models trained solely on simulated system matrices generalized to measured data across all tasks: for denoising, DnCNN/RDN/SwinIR outperformed DCT-F baseline by >10 dB PSNR and up to 0.1 SSIM on simulations and led to perceptually better reconstuctions of real data; for 2D upsampling, SMRnet exceeded bicubic by 20 dB PSNR and 0.08 SSIM at $\times 2$-$\times 4$ which did not transfer qualitatively to real measurements. For 3D accelerated calibration, SMRnet matched tricubic in noiseless cases and was more robust under noise, and for 3D inpainting, biharmonic inpainting was superior when noise-free but degraded with noise, while a PConvUNet maintained quality and yielded less blurry reconstructions. The demonstrated transferability of deep learning models trained on simulations to real measurements mitigates the data-scarcity problem and enables the development of new methods beyond current measurement capabilities.

Figures (6)

• Figure 1: Simulated 2D SM at the frequency $f=99.5$kHz illustrating variations across parameter groups: anisotropy constant (particle), DF amplitude (scanner), and calibration FOV (calibration). Unless stated otherwise, parameters are fixed to $d_{\text{P}}=20\,\unit{nm}$, $K^{\text{anis}}=3.2\,\unit{J.m^{-3}.10^3}$, $q=1$, $\bm{n}=[\cos(-3\pi/4),\,\sin(-3\pi/4)]$, $A_x=A_y=10\,\unit{mT.\mu_0^{-1}}$, $G_x=G_y=0.8\,\unit{T.m^{-1}.\mu_0^{-1}}$, $\mathrm{FOV}^{\mathrm{calib}}_x=\mathrm{FOV}^{\mathrm{calib}}_y=4A_x/G_x$, and $N^{\mathrm{calib}}_x=N^{\mathrm{calib}}_y=7\cdot \mathrm{FOV}^{\mathrm{calib}}_x/R^{\mathrm{FWHM}}_x$.
• Figure 2: Photographs of the phantoms used for evaluation: (a) snake (denoising); (b) resolution (accelerated calibration); (c) spiral (upsampling); and (d) rectangular (inpainting).
• Figure 3: Comparison of denoising methods (DCT-F, DnCNN, RDN, RDN-Langevin, and SwinIR) on a measured 2D SM corresponding to the snake phantom. Selected frequency components from receive coil $l=2$ and corresponding reconstructions are shown in the $xy$-plane.
• Figure 4: Comparison of tricubic interpolation and SMRnet for restoring a downsampled measured 3D SM corresponding to the resolution phantom. Selected frequency components from receive coils $l \in \{1, 2, 3\}$ in $xy$-plane and central slices of the reconstructions in the $xy$-, $xz$-, and $yz$-planes are shown.
• Figure 5: Comparison of bicubic interpolation and SMRnet for upsampling a measured 2D SM of the spiral phantom after SwinIR denoising. Selected frequency components from receive coils $l \in \{1, 2, 3\}$ and reconstructions are shown for both methods at factors 2.0 and 4.