A wavelet-based sparse row-action method for image reconstruction in magnetic particle imaging

Accurate Concentration Recovery for Quantitative Magnetic Particle Imaging Reconstruction via Nonconvex Regularization

Magnetic particle imaging (MPI) uses nonlinear response signals to noninvasively detect magnetic nanoparticles in space, and its quantitative properties hold promise for future precise quantitative treatments. In reconstruction, the system matrix based method necessitates suitable regularization terms, such as Tikhonov or non-negative fused lasso (NFL) regularization, to stabilize the solution. While NFL regularization offers clearer edge information than Tikhonov regularization, it carries a biased estimate of the l1 penalty, leading to an underestimation of the reconstructed concentration and adversely affecting the quantitative properties. In this paper, a new nonconvex regularization method including min-max concave (MC) and total variation (TV) regularization is proposed. This method utilized MC penalty to provide nearly unbiased sparse constraints and adds the TV penalty to provide a uniform intensity distribution of images. By combining the alternating direction multiplication method (ADMM) and the two-step parameter selection method, a more accurate quantitative MPI reconstruction was realized. The performance of the proposed method was verified on the simulation data, the Open-MPI dataset, and measured data from a homemade MPI scanner. The results indicate that the proposed method achieves better image quality while maintaining the quantitative properties, thus overcoming the drawback of intensity underestimation by the NFL method while providing edge information. In particular, for the measured data, the proposed method reduced the relative error in the intensity of the reconstruction results from 28% to 8%.

A greedy regularized block Kaczmarz method for accelerating reconstruction in magnetic particle imaging

Objective.Magnetic particle imaging (MPI) is an emerging medical tomographic imaging modality that enables real-time imaging with high sensitivity and high spatial and temporal resolution. For the system matrix reconstruction method, the MPI reconstruction problem is an ill-posed inverse problem that is commonly solved using the Kaczmarz algorithm. However, the high computation time of the Kaczmarz algorithm, which restricts MPI reconstruction speed, has limited the development of potential clinical applications for real-time MPI. In order to achieve fast reconstruction in real-time MPI, we propose a greedy regularized block Kaczmarz method (GRBK) which accelerates MPI reconstruction.Approach.GRBK is composed of a greedy partition strategy for the system matrix, which enables preprocessing of the system matrix into well-conditioned blocks to facilitate the convergence of the block Kaczmarz algorithm, and a regularized block Kaczmarz algorithm, which enables fast and accurate MPI image reconstruction at the same time.Main results.We quantitatively evaluated our GRBK using simulation data from three phantoms at 20 dB, 30 dB, and 40 dB noise levels. The results showed that GRBK can improve reconstruction speed by single orders of magnitude compared to the prevalent regularized Kaczmarz algorithm including Tikhonov regularization, the non-negative Fused Lasso, and wavelet-based sparse model. We also evaluated our method on OpenMPIData, which is real MPI data. The results showed that our GRBK is better suited for real-time MPI reconstruction than current state-of-the-art reconstruction algorithms in terms of reconstruction speed as well as image quality.Significance.Our proposed method is expected to be the preferred choice for potential applications of real-time MPI.

A fused LASSO operator for fast 3D magnetic particle imaging reconstruction

Objective.Magnetic particle imaging (MPI) is a promising imaging modality that leverages the nonlinear magnetization behavior of superparamagnetic iron oxide nanoparticles to determine their concentration distribution. Previous optimization models with multiple regularization terms have been proposed to achieve high-quality MPI reconstruction, but these models often result in increased computational burden, particularly for dense gridding 3D fields of view. In order to achieve faster reconstruction speeds without compromising reconstruction quality, we have developed a novel fused LASSO operator, total sum-difference (TSD), which effectively captures the sparse and smooth priors of MPI images.Methods.Through an analysis-synthesis equivalence strategy and a constraint smoothing strategy, the TSD regularized model was solved using the fast iterative soft-thresholding algorithm (FISTA). The resulting reconstruction method, TSD-FISTA, boasts low computational complexity and quadratic convergence rate over iterations.Results.Experimental results demonstrated that TSD-FISTA required only 10% and 37% of the time to achieve comparable or superior reconstruction quality compared to commonly used fused LASSO-based alternating direction method of multipliers and Tikhonov-based algebraic reconstruction techniques, respectively.Significance.TSD-FISTA shows promise for enabling real-time 3D MPI reconstruction at high frame rates for large fields of view.

DERnet: a deep neural network for end-to-end reconstruction in magnetic particle imaging

Objective. Magnetic particle imaging (MPI) shows potential for contributing to biomedical research and clinical practice. However, MPI images are effectively affected by noise in the signal as its reconstruction is an ill-posed inverse problem. Thus, effective reconstruction method is required to reduce the impact of the noise while mapping signals to MPI images. Traditional methods rely on the hand-crafted data-consistency (DC) term and regularization term based on spatial priors to achieve noise-reducing and reconstruction. While these methods alleviate the ill-posedness and reduce noise effects, they may be difficult to fully capture spatial features.Approach. In this study, we propose a deep neural network for end-to-end reconstruction (DERnet) in MPI that emulates the DC term and regularization term using the feature mapping subnetwork and post-processing subnetwork, respectively, but in a data-driven manner. By doing so, DERnet can better capture signal and spatial features without relying on hand-crafted priors and strategies, thereby effectively reducing noise interference and achieving superior reconstruction quality.Main results. Our data-driven method outperforms the state-of-the-art algorithms with an improvement of 0.9-8.8 dB in terms of peak signal-to-noise ratio under various noise levels. The result demonstrates the advantages of our approach in suppressing noise interference. Furthermore, DERnet can be employed for measured data reconstruction with improved fidelity and reduced noise. In conclusion, our proposed method offers performance benefits in reducing noise interference and enhancing reconstruction quality by effectively capturing signal and spatial features.Significance. DERnet is a promising candidate method to improve MPI reconstruction performance and facilitate its more in-depth biomedical application.

First Superferromagnetic Remanence Characterization and Scan Optimization for Super-Resolution Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a sensitive, high-contrast tracer modality that images superparamagnetic iron oxide nanoparticles, enabling radiation-free theranostic imaging. MPI resolution is currently limited by scanner and particle constraints. Recent tracers have experimentally shown 10× resolution and signal improvements with dramatically sharper M-H curves. Experiments show a dependence on interparticle interactions, conforming to literature definitions of superferromagnetism. We thus call our tracers superferromagnetic iron oxide nanoparticles (SFMIOs). While SFMIOs provide excellent signal and resolution, they exhibit hysteresis with non-negligible remanence and coercivity. We provide the first quantitative measurements of SFMIO remanence decay and reformation using a novel multiecho pulse sequence. We characterize MPI scanning with remanence decay and coercivity and describe an SNR-optimized pulse sequence for SFMIOs under human electromagnetic safety limitations. The resolution from SFMIOs could enable clinical MPI with 10× reduced scanner selection fields, reducing hardware costs by up to 100×.

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.

Magnetic particle imaging: tracer development and the biomedical applications of a radiation-free, sensitive, and quantitative imaging modality

Magnetic particle imaging (MPI) is an emerging tracer-based modality that enables real-time three-dimensional imaging of the non-linear magnetisation produced by superparamagnetic iron oxide nanoparticles (SPIONs), in the presence of an external oscillating magnetic field. As a technique, it produces highly sensitive radiation-free tomographic images with absolute quantitation. Coupled with a high contrast, as well as zero signal attenuation at-depth, there are essentially no limitations to where that can be imaged within the body. These characteristics enable various biomedical applications of clinical interest. In the opening sections of this review, the principles of image generation are introduced, along with a detailed comparison of the fundamental properties of this technique with other common imaging modalities. The main feature is a presentation on the up-to-date literature for the development of SPIONs tailored for improved imaging performance, and developments in the current and promising biomedical applications of this emerging technique, with a specific focus on theranostics, cell tracking and perfusion imaging. Finally, we will discuss recent progress in the clinical translation of MPI. As signal detection in MPI is almost entirely dependent on the properties of the SPION employed, this work emphasises the importance of tailoring the synthetic process to produce SPIONs demonstrating specific properties and how this impacts imaging in particular applications and MPI's overall performance.

Fast MPI reconstruction with non-smooth priors by stochastic optimization and data-driven splitting

Magnetic particle images are currently most often reconstructed using classical Tikhonov regularization (i.e. anℓ²regularization term) combined with Kaczmarz method. Quality enhancing choices like sparsity promotingℓ¹-regularization or TV regularization lead to problems that cannot be solved by standard Kaczmarz method. We propose to use stochastic primal-dual hybrid gradient method to gain more flexibility concerning the choice of data fitting term and regularization, respectively, and still obtain an algorithm which is at least as fast as Kaczmarz method. The proposed algorithm performs comparably to the current state-of-the-art method in terms of run time. The quality of reconstructions can be significantly improved as different regularization terms can be easily integrated. Moreover, in order to achieve further speed up of the method, we propose two new step size rules which lead to fast convergence and make the algorithm very easy to handle. We improve the performance of the algorithm further by applying a data-driven splitting scheme leading to a significant speed-up during the first iterations.