Learning-based reconstruction methods for magnetic particle imaging

Magnetic particle imaging (MPI) is a novel modality for imaging of magnetic nanoparticles (MNP) with high resolution, contrast and frame rate. An inverse problem is usually cased for reconstruction, which requires a time-consuming calibration scan for measuring a system matrix (SM). Previous calibration procedures involve scanning an MNP filled sample with a size that matches desired resolution through field of view. This time-consuming calibration scan which accounts for both system and MNP response imperfections is a critical factor prohibiting its practical use. Moreover, the quality of the reconstructed images heavily depend on the prior information about the MNP distribution as well as the specific re-construction algorithm, since the inverse problem is highly ill-posed. Previous approaches commonly solve an optimization problem based on the measurement model that iteratively estimates the image while enforcing data consistency in an interleaved fashion. However, while conventional hand-crated priors do not fully capture the underlying complex features of MPI images, recently proposed learned priors suffer from limited generalization performance. To tackle these issues, we first propose a deep learning based technique for accelerated MPI calibration. The technique utilizes transformers for SM super-resolution (TranSMS) for accelerated calibration of SMs with high signal-to-noise-ratio. For signal-to-noise-ratio efficiency, we propose scanning a low resolution SM with larger MNP sample size. For improved SM estimation, TranSMS leverages the vision trans-former to capture global contextual information while utilizing the convolutional module for local high-resolution features. Finally, a novel data-consistency module enforces measurement fidelity. TranSMS is shown to outperform competing methods significantly in terms of both SM recovery and image reconstruction performance. Next, to improve image reconstruction quality, we propose a novel physics-driven deep equilibrium based technique with learned consistency block for MPI (DEQ-MPI). DEQ-MPI embeds deep network operators into iterative optimization procedures for improved modeling of image statistics. Moreover, DEQ-MPI utilizes learned consistency to better capture the data statistics which helps improve the overall image reconstruction performance. Finally, compared to previous unrolling-based techniques, DEQ-MPI leverages implicit layers which enables training on the converged output. Demonstrations on both simulated and experimental data show that DEQ-MPI significantly improves image quality and reconstruction time over state-of-the-art reconstructions based on hand-crafted or learned priors.