Rethinking the Fourier Transform: Frequency Split-Enhance Network for Fast System Matrix Calibration in Magnetic Particle Image

Magnetic particle imaging (MPI) is an emerging molecular tomographic technique known for its high sensitivity and spatiotemporal resolution. Typically, high-quality images are obtained using the system matrix (SM)-based reconstruction method. Unlike other tomographic methods, SM calibration in MPI requires a time-consuming process to measure voxel-level responses across the MPI scanner’s field of view. Since the image resolution is directly affected by the size of the SM, the need for full-size SM calibration presents challenges for practical applications. This issue is further compounded by the necessity for repeated recalibration when changes occur in the tracer’s characteristics or the magnetic field environment. Consequently, efficient and rapid SM calibration is crucial. Existing calibration approaches often assume that each voxel in the SM is independent, overlooking the intrinsic relationships between voxels and their frequency-domain sparsity. To address this, we propose a novel framework dubbed frequency split-enhance network (FSE-Net), wherein the Fourier transform driven feature modulation block, the frequency split-enhance module (FSEM), is introduced to simultaneously split and enhance high- and low frequency features in distinct ways. By effectively capturing and utilizing frequency-domain features from a low-resolution (LR) SM obtained through fast sparse sampling, FSE-Net bridges the gap between LR and high-resolution (HR) volumetric images, achieving HR images with accurate shapes and refined textures. Extensive experiments on widely used OpenMPI public benchmark and simulation datasets demonstrate that our FSE-Net outperforms existing methods, achieving state-of-the-art performance in SM calibration tasks. Furthermore, FSE-Net significantly improves the resolution of an in-house field-free point (FFP) MPI system without requiring time-consuming full-size SM calibration, providing an efficient and practical solution for real-world applications.