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.

Unsupervised Medical Image Translation With Adversarial Diffusion Models.

Imputation of missing images via source-to-target modality translation can improve diversity in medical imaging protocols. A pervasive approach for synthesizing target images involves one-shot mapping through generative adversarial networks (GAN). Yet, GAN models that implicitly characterize the image distribution can suffer from limited sample fidelity. Here, we propose a novel method based on adversarial diffusion modeling, SynDiff, for improved performance in medical image translation. To capture a direct correlate of the image distribution, SynDiff leverages a conditional diffusion process that progressively maps noise and source images onto the target image. For fast and accurate image sampling during inference, large diffusion steps are taken with adversarial projections in the reverse diffusion direction. To enable training on unpaired datasets, a cycle-consistent architecture is devised with coupled diffusive and non-diffusive modules that bilaterally translate between two modalities. Extensive assessments are reported on the utility of SynDiff against competing GAN and diffusion models in multi-contrast MRI and MRI-CT translation. Our demonstrations indicate that SynDiff offers quantitatively and qualitatively superior performance against competing baselines.

Adaptive diffusion priors for accelerated MRI reconstruction.

Deep MRI reconstruction is commonly performed with conditional models that de-alias undersampled acquisitions to recover images consistent with fully-sampled data. Since conditional models are trained with knowledge of the imaging operator, they can show poor generalization across variable operators. Unconditional models instead learn generative image priors decoupled from the operator to improve reliability against domain shifts related to the imaging operator. Recent diffusion models are particularly promising given their high sample fidelity. Nevertheless, inference with a static image prior can perform suboptimally. Here we propose the first adaptive diffusion prior for MRI reconstruction, AdaDiff, to improve performance and reliability against domain shifts. AdaDiff leverages an efficient diffusion prior trained via adversarial mapping over large reverse diffusion steps. A two-phase reconstruction is executed following training: a rapid-diffusion phase that produces an initial reconstruction with the trained prior, and an adaptation phase that further refines the result by updating the prior to minimize data-consistency loss. Demonstrations on multi-contrast brain MRI clearly indicate that AdaDiff outperforms competing conditional and unconditional methods under domain shifts, and achieves superior or on par within-domain performance.

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.

A Simulation Study for Three Dimensional Tomographic Field Free Line Magnetic Particle Imaging.

Magnetic Particle Imaging (MPI) is an emerging modality that images the magnetic nanoparticle distribution inside the body. The method is based on the non-linear response of the magnetic nanoparticles to an applied magnetic field. In this study, we present simulation results for three-dimensional (3D) tomographic imaging using an open-bore MPI system that can electronically scan a field free line (FFL). A field of view with 26×26×10 mm3 volume is imaged with a relatively low gradient field of 0.5 T/m. Imaging results for two 3D phantoms are presented: a letter phantom and a vessel phantom with stenosis regions. Using the system-matrix based reconstruction approach, the images were obtained with the Algebraic reconstruction technique (ART) and alternating direction method of multipliers (ADMM) methods. The stenosis regions were visually recognizable in high SNR conditions with ADMM. The effect of low gradient strength became prominent with increasing noise level, resulting in interlayer coupling artifacts.Clinical relevance- Magnetic Particle Imaging (MPI) is a new tracer-based imaging modality with high-spatiotemporal resolution. MPI can map quantitative distribution of super-paramagnetic iron oxide nanoparticles introduced inside the body. A field free line scanning MPI system with an open configuration can enable imaging of human-size volumes for interventional operations. In this study, we present simulation results for an FFL scanning open MPI system configuration to scan 3D field of view volume electronically. We analyze 3D imaging performance for various SNR levels at a low gradient value of 0.5 T/m that is relevant for clinical-size systems.

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.

Tomographic Field Free Line Magnetic Particle Imaging With an Open-Sided Scanner Configuration.

Superparamagnetic iron oxide nanoparticles (SPIONs) have a high potential for use in clinical diagnostic and therapeutic applications. In vivo distribution of SPIONs can be imaged with the Magnetic Particle Imaging (MPI) method, which uses an inhomogeneous magnetic field with a field free region (FFR). The spatial distribution of the SPIONs are obtained by scanning the FFR inside the field of view (FOV) and sensing SPION related magnetic field disturbance. MPI magnets can be configured to generate a field free point (FFP), or a field free line (FFL) to scan the FOV. FFL scanners provide more sensitivity, and are also more suitable for scanning large regions compared to FFP scanners. Interventional procedures will benefit greatly from FFL based open magnet configurations. Here, we present the first open-sided MPI system that can electronically scan the FOV with an FFL to generate tomographic MPI images. Magnetic field measurements show that FFL can be rotated electronically in the horizontal plane and translated in three dimensions to generate 3D MPI images. Using the developed scanner, we obtained 2D images of dot and cylinder phantoms with varying iron concentrations between 11 [Formula: see text]/ml and 770 [Formula: see text]/ml. We used a measurement based system matrix image reconstruction method that minimizes l1 -norm and total variation in the images. Furthermore, we present 2D imaging results of two 4 mm-diameter vessel phantoms with 0% and 75% stenosis. The experiments show high quality imaging results with a resolution down to 2.5 mm for a relatively low gradient field of 0.6 T/m.

Simultaneous use of individual and joint regularization terms in compressive sensing: Joint reconstruction of multi-channel multi-contrast MRI acquisitions.

Multi-contrast images are commonly acquired together to maximize complementary diagnostic information, albeit at the expense of longer scan times. A time-efficient strategy to acquire high-quality multi-contrast images is to accelerate individual sequences and then reconstruct undersampled data with joint regularization terms that leverage common information across contrasts. However, these terms can cause features that are unique to a subset of contrasts to leak into the other contrasts. Such leakage-of-features may appear as artificial tissues, thereby misleading diagnosis. The goal of this study is to develop a compressive sensing method for multi-channel multi-contrast magnetic resonance imaging (MRI) that optimally utilizes shared information while preventing feature leakage. Joint regularization terms group sparsity and colour total variation are used to exploit common features across images while individual sparsity and total variation are also used to prevent leakage of distinct features across contrasts. The multi-channel multi-contrast reconstruction problem is solved via a fast algorithm based on Alternating Direction Method of Multipliers. The proposed method is compared against using only individual and only joint regularization terms in reconstruction. Comparisons were performed on single-channel simulated and multi-channel in-vivo datasets in terms of reconstruction quality and neuroradiologist reader scores. The proposed method demonstrates rapid convergence and improved image quality for both simulated and in-vivo datasets. Furthermore, while reconstructions that solely use joint regularization terms are prone to leakage-of-features, the proposed method reliably avoids leakage via simultaneous use of joint and individual terms, thereby holding great promise for clinical use.

Fast System Calibration With Coded Calibration Scenes for Magnetic Particle Imaging.

Magnetic particle imaging (MPI) is a relatively new medical imaging modality, which detects the nonlinear response of magnetic nanoparticles (MNPs) that are exposed to external magnetic fields. The system matrix (SM) method for MPI image reconstruction requires a time consuming system calibration scan prior to image acquisition, where a single MNP sample is measured at each voxel position in the field-of-view (FOV). The scanned sample has the maximum size of a voxel so that the calibration measurements have relatively poor signal-to-noise ratio (SNR). In this paper, we present the coded calibration scene (CCS) framework, where we place multiple MNP samples inside the FOV in a random or pseudo-random fashion. Taking advantage of the sparsity of the SM, we reconstruct the SM by solving a convex optimization problem with alternating direction method of multipliers using CCS measurements. We analyze the effects of filling rate, number of measurements, and SNR on the SM reconstruction using simulations and demonstrate different implementations of CCS for practical realization. We also compare the imaging performance of the proposed framework with that of a standard compressed sensing SM reconstruction that utilizes a subset of calibration measurements from a single MNP sample. The results show that CCS significantly reduces calibration time while increasing both the SM reconstruction and image reconstruction performances.

Trajectory analysis for field free line magnetic particle imaging.

PURPOSE: Magnetic particle imaging (MPI) is a relatively new method to image the spatial distribution of magnetic nanoparticle (MNP) tracers administered to the body with high spatial and temporal resolution using an inhomogeneous magnetic field. The spatial information of the MNP's is encoded using a field free point (FFP), or a field free line (FFL), in which the magnetic field vanishes at a point, or on a line, respectively. FFL scanning has the advantage of improved sensitivity compared to FFP scanning as a result of higher signal-to-noise ratio. The trajectory traversed by the FFL or FFP is an important parameter of the MPI system and should be selected to achieve the best imaging quality in minimum scan time, while considering hardware constraints and patient safety. In this study, we analyzed the image quality of different FFL trajectories for a large field of view (FOV) using simulations, to provide a baseline information for FFL scanning MPI system design. METHODS: We simulated a human-sized FFL scanning MPI configuration to image a circular FOV with 160 mm diameter, and compared Radial, Spiral, Uniform Spiral, Flower, and Lissajous trajectories with different trajectory densities scanned by the FFL for constant scan time. We analyzed the system matrices of the trajectories in terms of mutual coherence and homogeneity of the spatial sensitivity. We calculated the maximum electric fields induced on a homogeneous conductive body by the selection field (SF) and the focus field (FF) to compare the trajectories based on the nerve stimulation threshold. The images were obtained using the system matrix reconstruction approach with two different image reconstruction methods. In the first one, we used the conventional image reconstruction method, algebraic reconstruction technique (ART), which gives a regularized least-squares solution. In the second one, we used the state-of-the-art alternating direction method of multipliers (ADMM), which minimizes a weighted sum of the l1 -norm and the total variation (TV) of the images. RESULTS: The Radial and Spiral trajectories resulted in a poor imaging performance at low trajectory densities due to relatively high coherency and poor sensitivity of the measurements, respectively. For ART reconstruction, the highest image quality with the lowest trajectory density was achieved with the Uniform Spiral trajectory. Uniform Spiral, Flower, and Lissajous trajectories yielded comparable performance with ADMM reconstruction. The rotating SF induced higher electric field amplitude compared to the FF. Consequently, maximum allowable gradient at the same trajectory density was greater for the Radial trajectory compared to the other trajectories. CONCLUSIONS: For a large FOV coverage, the Uniform Spiral trajectory offers a good compromise between image quality and imaging time, taking safety and hardware limitations into account. The Radial trajectory, especially using l1 -norm and TV priors in the reconstruction, may be favorable in case the SF induced electric field is higher than that of the FF at the same frequency (e.g., relatively small FOV coverage). In general, ADMM reconstruction resulted in higher contrast and resolution compared to ART, leading to lighter requirements on the density of the trajectory.

Statistically Segregated k-Space Sampling for Accelerating Multiple-Acquisition MRI.

A central limitation of multiple-acquisition magnetic resonance imaging (MRI) is the degradation in scan efficiency as the number of distinct datasets grows. Sparse recovery techniques can alleviate this limitation via randomly undersampled acquisitions. A frequent sampling strategy is to prescribe for each acquisition a different random pattern drawn from a common sampling density. However, naive random patterns often contain gaps or clusters across the acquisition dimension that, in turn, can degrade reconstruction quality or reduce scan efficiency. To address this problem, a statistically segregated sampling method is proposed for multiple-acquisition MRI. This method generates multiple patterns sequentially while adaptively modifying the sampling density to minimize k-space overlap across patterns. As a result, it improves incoherence across acquisitions while still maintaining similar sampling density across the radial dimension of k-space. Comprehensive simulations and in vivo results are presented for phase-cycled balanced steady-state free precession and multi-echo [Formula: see text]-weighted imaging. Segregated sampling achieves significantly improved quality in both Fourier and compressed-sensing reconstructions of multiple-acquisition datasets.