DEQ-MPI: A Deep Equilibrium Reconstruction With Learned Consistency for Magnetic Particle Imaging.

Magnetic particle imaging (MPI) offers unparalleled contrast and resolution for tracing magnetic nanoparticles. A common imaging procedure calibrates a system matrix (SM) that is used to reconstruct data from subsequent scans. The ill-posed reconstruction problem can be solved by simultaneously enforcing data consistency based on the SM and regularizing the solution based on an image prior. Traditional hand-crafted priors cannot capture the complex attributes of MPI images, whereas recent MPI methods based on learned priors can suffer from extensive inference times or limited generalization performance. Here, we introduce a novel physics-driven method for MPI reconstruction based on a deep equilibrium model with learned data consistency (DEQ-MPI). DEQ-MPI reconstructs images by augmenting neural networks into an iterative optimization, as inspired by unrolling methods in deep learning. Yet, conventional unrolling methods are computationally restricted to few iterations resulting in non-convergent solutions, and they use hand-crafted consistency measures that can yield suboptimal capture of the data distribution. DEQ-MPI instead trains an implicit mapping to maximize the quality of a convergent solution, and it incorporates a learned consistency measure to better account for the data distribution. Demonstrations on simulated and experimental data indicate that DEQ-MPI achieves superior image quality and competitive inference time to state-of-the-art MPI reconstruction methods.

TranSMS: Transformers for Super-Resolution Calibration in Magnetic Particle Imaging.

Magnetic particle imaging (MPI) offers exceptional contrast for magnetic nanoparticles (MNP) at high spatio-temporal resolution. A common procedure in MPI starts with a calibration scan to measure the system matrix (SM), which is then used to set up an inverse problem to reconstruct images of the MNP distribution during subsequent scans. This calibration enables the reconstruction to sensitively account for various system imperfections. Yet time-consuming SM measurements have to be repeated under notable changes in system properties. Here, we introduce a novel deep learning approach for accelerated MPI calibration based on Transformers for SM super-resolution (TranSMS). Low-resolution SM measurements are performed using large MNP samples for improved signal-to-noise ratio efficiency, and the high-resolution SM is super-resolved via model-based deep learning. TranSMS leverages a vision transformer module to capture contextual relationships in low-resolution input images, a dense convolutional module for localizing high-resolution image features, and a data-consistency module to ensure measurement fidelity. Demonstrations on simulated and experimental data indicate that TranSMS significantly improves SM recovery and MPI reconstruction for up to 64-fold acceleration in two-dimensional imaging.

Deep Learned Super Resolution of System Matrices for Magnetic Particle Imaging.

Magnetic Particle Imaging (MPI) is a new imaging technique that allows high resolution & high frame-rate imaging of magnetic nanoparticles (MNP). It relies on the nonlinear response of MNPs under a magnetic field. The imaging process can be modeled linearly, and then image reconstruction can be case as an inverse problem using a measured system matrix (SM). However, this calibration measurement is time consuming so it reduces practicality. In this study, we proposed a novel method for accelerating the SM calibration based on joint super-resolution (SR) and denoising of sensitivty maps (i.e., rows of SM). The proposed method is based on a deep convolutional neural network (CNN) architecture with residual-dense blocks. Model training was performed using noisy SM measurements simulated for varying MNP size and gradient strengths. Comparisons were performed against conventional low-resolution SM calibration, noisy high-resolution SM calibration, and bicubic upsampling of low-resolution SM. We show that the proposed method improves high-resolution SM recovery, and in turn leads to improved resolution and quality in subsequently reconstructed MPI images.