Trajectory optimized NUFFT: Faster non-Cartesian MRI reconstruction through prior knowledge and parallel architectures

Series of first-order phase shifts correct lattice reduction of fractional K-space indices

Lattice reduction of K-space acquisition at fractional indices refers to reducing the indices to the smallest nearby integer, thereby generating a Cartesian grid, allowing subsequent inverse Fourier Transformation. For band-limited signals, we show that the error in lattice reduction is equivalent to first order phase shifts, which in the infinite limit approaches W∞=φ(cotφ-i), where φ is a first-order phase shift vector. In general, the inverse corrections can be specified from the binary representation of the fractional part of the K-space indices. For non-uniform sparsity, we show how to incorporate the inverse corrections into compressed sensing reconstructions.

Golden-Angle Radial MRI: Basics, Advances, and Applications

In recent years, golden‐angle radial sampling has received substantial attention and interest in the magnetic resonance imaging (MRI) community, and it has become a popular sampling trajectory for both research and clinical use. However, although the number of relevant techniques and publications has grown rapidly, there is still a lack of a review paper that provides a comprehensive overview and summary of the basics of golden‐angle rotation, the advantages and challenges/limitations of golden‐angle radial sampling, and recommendations in using different types of golden‐angle radial trajectories for MRI applications. Such a review paper is expected to be helpful both for clinicians who are interested in learning the potential benefits of golden‐angle radial sampling and for MRI physicists who are interested in exploring this research direction. The main purpose of this review paper is thus to present an overview and summary about golden‐angle radial MRI sampling. The review consists of three sections. The first section aims to answer basic questions such as: what is a golden angle; how is the golden angle calculated; why is golden‐angle radial sampling useful, and what are its limitations. The second section aims to review more advanced trajectories of golden‐angle radial sampling, including tiny golden‐angle rotation, stack‐of‐stars golden‐angle radial sampling, and three‐dimensional (3D) kooshball golden‐angle radial sampling. Their respective advantages and limitations and potential solutions to address these limitations are also discussed. Finally, the third section reviews MRI applications that can benefit from golden‐angle radial sampling and provides recommendations to readers who are interested in implementing golden‐angle radial trajectories in their MRI studies.

An end-to-end-trainable iterative network architecture for accelerated radial multi-coil 2D cine MR image reconstruction

PURPOSE

Iterative convolutional neural networks (CNNs) which resemble unrolled learned iterative schemes have shown to consistently deliver state-of-the-art results for image reconstruction problems across different imaging modalities. However, because these methods include the forward model in the architecture, their applicability is often restricted to either relatively small reconstruction problems or to problems with operators which are computationally cheap to compute. As a consequence, they have not been applied to dynamic non-Cartesian multi-coil reconstruction problems so far.

METHODS

In this work, we propose a CNN architecture for image reconstruction of accelerated 2D radial cine MRI with multiple receiver coils. The network is based on a computationally light CNN component and a subsequent conjugate gradient (CG) method which can be jointly trained end-to-end using an efficient training strategy. We investigate the proposed training strategy and compare our method with other well-known reconstruction techniques with learned and non-learned regularization methods.

RESULTS

Our proposed method outperforms all other methods based on non-learned regularization. Further, it performs similar or better than a CNN-based method employing a 3D U-Net and a method using adaptive dictionary learning. In addition, we empirically demonstrate that even by training the network with only iteration, it is possible to increase the length of the network at test time and further improve the results.

CONCLUSIONS

End-to-end training allows to highly reduce the number of trainable parameters of and stabilize the reconstruction network. Further, because it is possible to change the length of the network at the test time, the need to find a compromise between the complexity of the CNN-block and the number of iterations in each CG-block becomes irrelevant.

Highly accelerated free-breathing real-time phase contrast cardiovascular MRI via complex-difference deep learning

PURPOSE

To develop and evaluate a real-time phase contrast (PC) MRI protocol via complex-difference deep learning (DL) framework.

METHODS

DL used two 3D U-nets to separately filter aliasing artifact from radial real-time velocity-compensated and complex-difference images. U-nets were trained with synthetic real-time PC generated from electrocardiograph (ECG) -gated, breath-hold, segmented PC (ECG-gated segmented PC) acquired at the ascending aorta of 510 patients. In 21 patients, free-breathing, ungated real-time (acceleration rate = 28.8) and ECG-gated segmented (acceleration rate = 2) PC were prospectively acquired at the ascending aorta. Hemodynamic parameters (cardiac output [CO], stroke volume [SV], and mean velocity at peak systole [peak mean velocity]) were measured for ECG-gated segmented and DL-filtered synthetic real-time PC and compared using Bland-Altman and linear regression analyses. Additionally, hemodynamic parameters were quantified from DL-filtered, compressed-sensing (CS) -reconstructed, and gridding reconstructed prospective real-time PC and compared to ECG-gated segmented PC.

RESULTS

Synthetic real-time PC with DL showed strong correlation (R > 0.98) and good agreement with ECG-gated segmented PC for quantified hemodynamic parameters (mean-difference: CO = -0.3 L/min, SV = -4.3 mL, peak mean velocity = -2.3 cm/s). On average, DL required 0.39 s/frame to filter prospective real-time PC, which was 4.6-fold faster than CS. Compared to CS, DL showed superior correlation, tighter limits of agreement (LOAs), better bias for peak mean velocity, and worse bias for CO and SV. Compared to gridding, DL showed similar correlation, tighter LOAs for CO and SV, similar bias for CO, and worse bias for SV and peak mean velocity.

CONCLUSION

The complex-difference DL framework accelerated real-time PC-MRI by nearly 28-fold, enabling rapid free-running real-time assessment of flow hemodynamics.

Non-contrast coronary magnetic resonance angiography: current frontiers and future horizons

Coronary magnetic resonance angiography (coronary MRA) is advantageous in its ability to assess coronary artery morphology and function without ionizing radiation or contrast media. However, technical limitations including reduced spatial resolution, long acquisition times, and low signal-to-noise ratios prevent it from clinical routine utilization. Nonetheless, each of these limitations can be specifically addressed by a combination of novel technologies including super-resolution imaging, compressed sensing, and deep-learning reconstruction. In this paper, we first review the current clinical use and motivations for non-contrast coronary MRA, discuss currently available coronary MRA techniques, and highlight current technical developments that hold unique potential to optimize coronary MRA image acquisition and post-processing. In the final section, we examine the various research-based coronary MRA methods and metrics that can be leveraged to assess coronary stenosis severity, physiological function, and atherosclerotic plaque characterization. We specifically discuss how such technologies may contribute to the clinical translation of coronary MRA into a robust modality for routine clinical use.

Strategies for rapid reconstruction in 3D MRI with radial data acquisition: 3D fast Fourier transform vs two-step 2D filtered back-projection

For 3D radial data reconstruction in magnetic resonance imaging (MRI), fast Fourier transform via gridding (gFFT) is widely used for its fast processing and flexibility. In comparison, conventional 3D filtered back projection (cFBP), while more robust against common radial k-space centering errors, suffers from long computation times and is less frequently used. In this study, we revisit another back-projection reconstruction strategy, namely two-step 2D filtered back-projection (tsFBP), as an alternative 3D radial MRI reconstruction method that combines computational efficiency and certain error tolerance. In order to compare the three methods (gFFT, cFBP, and tsFBP), theoretical analysis was performed to evaluate the number of computational steps involved in each method. Actual reconstruction times were also measured and compared using 3D radial-MRI data of a phantom and a human brain. Additionally, the sensitivity of tsFBP to artifacts caused by radial k-space centering errors was compared with the other methods. Compared to cFBP, tsFBP dramatically improved the reconstruction speed while retaining the benefit of tolerance to the radial k-space errors. Our study therefore suggests that tsFBP can be a promising alternative to the conventional back projection method for 3D radial MRI reconstruction.

Neural networks-based regularization for large-scale medical image reconstruction

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks (NNs) and cascaded NNs have been reported to achieve state-of-the-art results with respect to various quantitative quality measures as PSNR, NRMSE and SSIM across different imaging modalities. However, the fact that these approaches employ the application of the forward and adjoint operators repeatedly in the network architecture requires the network to process the whole images or volumes at once, which for some applications is computationally infeasible. In this work, we follow a different reconstruction strategy by strictly separating the application of the NN, the regularization of the solution and the consistency with the measured data. The regularization is given in the form of an image prior obtained by the output of a previously trained NN which is used in a Tikhonov regularization framework. By doing so, more complex and sophisticated network architectures can be used for the removal of the artefacts or noise than it is usually the case in iterative NNs. Due to the large scale of the considered problems and the resulting computational complexity of the employed networks, the priors are obtained by processing the images or volumes as patches or slices. We evaluated the method for the cases of 3D cone-beam low dose CT and undersampled 2D radial cine MRI and compared it to a total variation-minimization-based reconstruction algorithm as well as to a method with regularization based on learned overcomplete dictionaries. The proposed method outperformed all the reported methods with respect to all chosen quantitative measures and further accelerates the regularization step in the reconstruction by several orders of magnitude.

snapMRF: GPU-accelerated magnetic resonance fingerprinting dictionary generation and matching using extended phase graphs

PURPOSE

Magnetic resonance fingerprinting (MRF) is a state-of-the-art quantitative MRI technique with a computationally demanding reconstruction process, the accuracy of which depends on the accuracy of the signal model employed. Having a fast, validated, open-source MRF reconstruction would improve the dependability and accuracy of clinical applications of MRF.

METHODS

We parallelized both dictionary generation and signal matching on the GPU by splitting the simulation and matching of dictionary atoms across threads. Signal generation was modeled using both Bloch equation simulation and the extended phase graph (EPG) formalism. Unit tests were implemented to ensure correctness. The new package, snapMRF, was tested with a calibration phantom and an in vivo brain.

RESULTS

Compared with other online open-source packages, dictionary generation was accelerated by 10-1000× and signal matching by 10-100×. On a calibration phantom, T₁ and T₂ values were measured with relative errors that were nearly identical to those from existing packages when using the same sequence and dictionary configuration, but errors were much lower when using variable sequences that snapMRF supports but that competitors do not.

CONCLUSION

Our open-source package snapMRF was significantly faster and retrieved accurate parameters, possibly enabling real-time parameter map generation for small dictionaries. Further refinements to the acquisition scheme and dictionary setup could improve quantitative accuracy.

Trajectory optimized NUFFT: Faster non-Cartesian MRI reconstruction through prior knowledge and parallel architectures

Purpose

The non‐uniform fast Fourier transform (NUFFT) involves interpolation of non‐uniformly sampled Fourier data onto a Cartesian grid, an interpolation that is slowed by complex, non‐local data access patterns. A faster NUFFT would increase the clinical relevance of the plethora of advanced non‐Cartesian acquisition methods.

Methods

Here we customize the NUFFT procedure for a radial trajectory and GPU architecture to eliminate the bottlenecks encountered when allowing for arbitrary trajectories and hardware. We call the result TRON, for TRajectory Optimized NUFFT. We benchmark the speed and accuracy TRON on a Shepp‐Logan phantom and on whole‐body continuous golden‐angle radial MRI.

Results

TRON was 6–30× faster than the closest competitor, depending on test data set, and was the most accurate code tested.

Conclusions

Specialization of the NUFFT algorithm for a particular trajectory yielded significant speed gains. TRON can be easily extended to other trajectories, such as spiral and PROPELLER. TRON can be downloaded at http://github.com/davidssmith/TRON.