Deep learning-enhanced X-space reconstruction for magnetic particle imaging: a physics-consistent approach

Magnetic particle imaging (MPI) is an emerging tracer-based imaging modality with high sensitivity and excellent temporal resolution; however, X-space reconstruction suffers from inherent point spread function (PSF) blur that limits spatial resolution. This study aims to improve X-space MPI reconstruction quality while preserving physical consistency. To address this problem, we propose X-Space-PC-Restore, a physics-consistent deep learning framework that combines a hybrid U-Net encoder-decoder architecture with Transformer-based attention and PSF-guided loss functions. The method was evaluated on a synthetic dataset of 1600 samples spanning 4 phantom types (line, circle, ellipse, cross), Lissajous trajectories, and signal-to-noise ratio (SNR) levels from 5 to 15 dB. The proposed model achieved a peak SNR (PSNR) of 15.48 dB and an normalized root mean square error (NRMSE) of 0.175, representing a 23.0% improvement in PSNR and 45.8% reduction in NRMSE compared to the best classical baseline (Richardson-Lucy: PSNR 12.58 dB, NRMSE 0.244). The method demonstrated consistent superiority across all tested SNR levels (5-40 dB), with PSNR gains ranging from 1.4 to 3.0 dB over Richardson-Lucy. Resolution analysis showed that Richardson-Lucy achieved the best full width at half maximum (10.47 ± 0.93 pixels), while the proposed method achieved near-ground-truth resolution. SNR robustness analysis confirmed stable performance of the proposed method across noise conditions, whereas classical methods exhibited greater sensitivity to noise. These results demonstrate that physics-informed deep learning is a promising strategy for reducing blur, improving fidelity, and enhancing the reliability of MPI image reconstruction.