Continuous implicit neural representation for arbitrary super-resolution of system matrix in magnetic particle imaging

<i>Objective</i>. Magnetic particle imaging (MPI) is a novel imaging technique that uses magnetic fields to detect tracer materials consisting of magnetic nanoparticles. System matrix (SM) based image reconstruction is essential for achieving high image quality in MPI. However, the time-consuming SM calibrations need to be repeated whenever the magnetic field's or nanoparticle's characteristics change. Accelerating this calibration process is therefore crucial. The most common acceleration approach involves undersampling during the SM calibration procedure, followed by super-resolution methods to recover the high-resolution SM. However, these methods typically require separate training of multiple models for different undersampling ratios, leading to increased storage and training time costs.<i>Approach</i>. We propose an arbitrary-scale SM super-resolution method based on continuous implicit neural representation (INR). Using INR, the SM is modeled as a continuous function in space, enabling arbitrary-scale super-resolution by sampling the function at different densities. A cross-frequency encoder is implemented to share SM frequency information and analyze contextual relationships, resulting in a more intelligent and efficient sampling strategy. Convolutional neural networks (CNNs) are utilized to learn and optimize the grid sampling process in INR, leveraging the advantage of CNNs in learning local feature associations and considering surrounding information comprehensively.<i>Main results</i>. Experimental results on OpenMPI demonstrate that our method outperforms existing methods and enables calibration at any scale with a single model. The proposed method achieves high accuracy and efficiency in SM recovery, even at high undersampling rates.<i>Significance</i>. The proposed method significantly reduces the storage and training time costs associated with SM calibration, making it more practical for real-world applications. By enabling arbitrary-scale super-resolution with a single model, our approach enhances the flexibility and efficiency of MPI systems, paving the way for more widespread adoption of MPI technology.