Low-spatial-frequency perception enhancing dynamic convolutional network for system matrix recovery in magnetic...

Magnetic particle imaging (MPI) is an emerging molecular imaging modality known for its high sensitivity and long-term tracking. System matrix (SM)-based image reconstruction is one of the most important reconstruction methods for MPI. However, MPI reconstruction based on the measured SM is limited by the requirement of voxel-stepwise precise calibration of system function within the field of view (FOV), which is time-consuming and noise-prone. Additionally, any changes in system properties require recalibrating the SM. This hinders the clinical translation and practical application of MPI.

To address these limitations, we propose a low-spatial-frequency perception enhancing dynamic convolutional network (LPEDCN) to recover SMs for accelerating calibration.

Specifically, we observe and reveal a positive correlation between the percentage of low-spatial-frequency energy and the signal-to-noise ratio (SNR) in the spatial Fourier transform (SFT) domain of real-world SM rows. Based on this prior, we design a low-spatial-frequency perception enhancement (LPE) joint loss to suppress high-frequency noise during model training. We also introduce a context-modulated dynamic convolution (CMDC) to capture long-range contextual features. We evaluate LPEDCN on simulated (training set: 60 SMs split into 107880 SM-row slices; validation set: 20 SMs split into 37520 slices; test set: 20 SMs split into 32660 slices; with no overlap between sets), public real-world OpenMPI (training set: 1 SM split into 101861 SM-row slices; validation set: 1 SM split into 62863 slices; test set: 1 SM split into 85347 slices; with no overlap between sets), and in-house (test set: 2 SMs split into 225 and 272 slices, respectively) datasets. SM recovery accuracy is evaluated by normalized root-mean-square error (nRMSE), and the reconstruction quality is evaluated by peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM). We assess LPEDCN by comparing it with seven state-of-the-art (SOTA) methods. Statistical significance is evaluated using two-tailed t-tests with p < 0.05 after False Discovery Rate (FDR) correction, and practical significance is assessed using Cohen's d for effect size.

LPEDCN not only accelerates SM calibration in MPI, but also exhibits higher accuracy in SM recovery and better quality in image reconstruction compared to SOTA methods. For the core SM recovery metric nRMSE, LPEDCN significantly outperforms SOTA methods (p < 0.05, FDR corrected) for 2×, 4×, and 8× super-resolution (SR), respectively, with effect size values of 0.23-1.02 on the simulated dataset and 0.06-45.63 on the public real-world OpenMPI dataset. For the image reconstruction metrics PSNR and SSIM, LPEDCN is significantly superior to SOTA methods (p < 0.05, FDR corrected) for 2×, 4×, and 8× SR, respectively, with effect size values of 0.45-8.68 on the simulated dataset, and 0.10-4.65 on the OpenMPI dataset. These quantitative results consistently verify that LPEDCN yields practically meaningful performance improvements. Additionally, LPEDCN greatly reduces the SM calibration time and achieves excellent high-resolution reconstruction images.

LPEDCN holds practical promise for improving MPI calibration efficiency.