Accelerating Non-Cartesian MRI Reconstruction Convergence Using k-Space Preconditioning

Quantifying spatial and dynamic lung abnormalities with 3D PREFUL FLORET UTE imaging: A feasibility study

PURPOSE

Pulmonary MRI faces challenges due to low proton density, rapid transverse magnetization decay, and cardiac and respiratory motion. The fermat-looped orthogonally encoded trajectories (FLORET) sequence addresses these issues with high sampling efficiency, strong signal, and motion robustness, but has not yet been applied to phase-resolved functional lung (PREFUL) MRI-a contrast-free method for assessing pulmonary ventilation during free breathing. This study aims to develop a reconstruction pipeline for FLORET UTE, enhancing spatial resolution for three-dimensional (3D) PREFUL ventilation analysis.

METHODS

The FLORET sequence was used to continuously acquire data over 7 ± 2 min in 36 participants, including healthy subjects (N = 7) and patients with various pulmonary conditions (N = 29). Data were reconstructed into respiratory images using motion-compensated low-rank reconstruction, and a 3D PREFUL algorithm was adapted to quantify static and dynamic ventilation surrogates. Image sharpness and signal-to-noise ratio were evaluated across different motion states. PREFUL ventilation metrics were compared with static 129Xe ventilation MRI.

RESULTS

Optimal image sharpness and accurate ventilation dynamics were achieved using 24 respiratory bins, leading to their use in the study. A strong correlation was found between 3D PREFUL FLORET UTE ventilation defect percentages (VDPs) and 129Xe VDPs (r ≥ 0.61, p < 0.0001), although PREFUL FLORET static VDPs were significantly higher (mean bias = -10.1%, p < 0.0001). In diseased patients, dynamic ventilation parameters showed greater heterogeneity and better alignment with 129Xe VDPs.

CONCLUSION

The proposed reconstruction pipeline for FLORET UTE MRI offers improved spatial resolution and strong correlation with 129Xe MRI, enabling dynamic ventilation quantification that may reveal airflow abnormalities in lung disease.

Dynamic MRI with Locally Low-Rank Subspace Constraint: Towards 1-Second Temporal Resolution Aided by Deep Learning

MRI is the most effective method for screening high-risk breast cancer patients. While current exams primarily rely on the qualitative evaluation of morphological features before and after contrast administration and less on contrast kinetic information, the latest developments in acquisition protocols aim to combine both. However, balancing between spatial and temporal resolution poses a significant challenge in dynamic MRI. Here, we propose a radial MRI reconstruction framework for Dynamic Contrast Enhanced (DCE) imaging, which offers a joint solution to existing spatial and temporal MRI limitations. It leverages a locally low-rank (LLR) subspace model to represent spatially localized dynamics based on tissue information. Our framework demonstrated substantial improvement in CNR, noise reduction and enables a flexible temporal resolution, ranging from a few seconds to 1-second, aided by a neural network, resulting in images with reduced undersampling penalties. Finally, our reconstruction framework also shows potential benefits for head and neck, and brain MRI applications, making it a viable alternative for a range of DCE-MRI exams.

Ex vivo imaging of subacute myocardial infarction with ultra-short echo time 3D quantitative T1- and T1ρ -mapping magnetic resonance imaging in mice

Aims

The aim of this study was to develop an ultra-short echo time 3D magnetic resonance imaging (MRI) method for imaging subacute myocardial infarction (MI) quantitatively and in an accelerated way. Here, we present novel 3D T1- and T1ρ -weighted Multi-Band SWeep Imaging with Fourier Transform and Compressed Sensing (MB-SWIFT-CS) imaging of subacute MI in mice hearts ex vivo.

Methods and results

Relaxation time-weighted and under-sampled 3D MB-SWIFT-CS MRI were tested with manganese chloride (MnCl2) phantom and mice MI model. MI was induced in C57BL mice, and the hearts were collected 7 days after MI and then fixated. The hearts were imaged with T1 and adiabatic T1ρ relaxation time-weighted 3D MB-SWIFT-CS MRI, and the contrast-weighted image series were estimated with a locally low-rank regularized subspace constrained reconstruction. The quantitative parameter maps, T1 and T1ρ , were then obtained by performing non-linear least squares signal fitting on the image estimates. For comparison, the hearts were also imaged using 2D fast spin echo-based T2 and T1ρ mapping methods. The relaxation rates varied linearly with the MnCl2 concentration, and the T1 and T1ρ relaxation time values were elevated in the damaged areas. The ischaemic areas could be observed visually in the 3D T1, 3D T1ρ , and 2D MRI maps. The scar tissue formation in the anterior wall of the left ventricle and inflammation in the septum were confirmed by histology, which is in line with the results of MRI.

Conclusion

MI with early fibrosis, increased inflammatory activity, and interstitial oedema were determined simultaneously with T1 and T1ρ relaxation time constants within the myocardium by using the 3D MB-SWIFT-CS method, allowing quantitative isotropic 3D assessment of the entire myocardium.

Three contrasts in 3 min: Rapid, high-resolution, and bone-selective UTE MRI for craniofacial imaging with automated deep-learning skull segmentation

PURPOSE

Ultrashort echo time (UTE) MRI can be a radiation-free alternative to CT for craniofacial imaging of pediatric patients. However, unlike CT, bone-specific MR imaging is limited by long scan times, relatively low spatial resolution, and a time-consuming bone segmentation workflow.

METHODS

A rapid, high-resolution UTE technique for brain and skull imaging in conjunction with an automatic segmentation pipeline was developed. A dual-RF, dual-echo UTE sequence was optimized for rapid scan time (3 min) and smaller voxel size (0.65 mm3). A weighted least-squares conjugate gradient method for computing the bone-selective image improves bone specificity while retaining bone sensitivity. Additionally, a deep-learning U-Net model was trained to automatically segment the skull from the bone-selective images. Ten healthy adult volunteers (six male, age 31.5 ± 10 years) and three pediatric patients (two male, ages 12 to 15 years) were scanned at 3 T. Clinical CT for the three patients were obtained for validation. Similarities in 3D skull reconstructions relative to clinical standard CT were evaluated based on the Dice similarity coefficient and Hausdorff distance. Craniometric measurements were used to assess geometric accuracy of the 3D skull renderings.

RESULTS

The weighted least-squares method produces images with enhanced bone specificity, suppression of soft tissue, and separation from air at the sinuses when validated against CT in pediatric patients. Dice similarity coefficient overlap was 0.86 ± 0.05, and the 95th percentile Hausdorff distance was 1.77 ± 0.49 mm between the full-skull binary masks of the optimized UTE and CT in the testing dataset.

CONCLUSION

An optimized MRI acquisition, reconstruction, and segmentation workflow for craniofacial imaging was developed.

Measurement of T1ρ dispersion with compressed sensing and magnetization prepared radial balanced steady-state free precession in spontaneous human osteoarthritis

PURPOSE

To assess the potential for accelerating continuous-wave (CW) T1ρ dispersion measurement with compressed sensing approach via studying the effect that the data reduction has on the ability to detect differences between intact and degenerated articular cartilage with different spin-lock amplitudes and to assess quantitative bias due to acceleration.

METHODS

Osteochondral plugs (n = 27, 4 mm diameter) from femur (n = 14) and tibia (n = 13) regions from human cadaver knee joints were obtained from commercial biobank (Science Care, USA) under Ethical permission 134/2015. MRI of specimens was performed at 9.4T with magnetization prepared radial balanced SSFP (bSSFP) readout sequence, and the CWT1ρ relaxation time maps were computed from the measured data. The relaxation time maps were evaluated in the cartilage zones for different acceleration factors. For reference, Osteoarthritis Research Society International (OARSI) grading and biomechanical measurements were performed and correlated with the MRI findings.

RESULTS

Four-fold acceleration of CWT1ρ dispersion measurement by compressed sensing approach was feasible without meaningful loss in the sensitivity to osteoarthritic (OA) changes within the articular cartilage. Differences were significant between intact and OA groups in the superficial and transitional zones, and CWT1ρ correlated moderately with the reference measurements (0.3 < r < 0.7).

CONCLUSION

CWT1ρ was able to differentiate between intact and OA cartilage even with four-fold acceleration. This indicates that acceleration of CWT1ρ dispersion measurement by compressed sensing approach is feasible with negligible loss in the sensitivity to osteoarthritic changes in articular cartilage.

A decay-modeled compressed sensing reconstruction approach for non-Cartesian hyperpolarized 129Xe MRI

PURPOSE

Hyperpolarized 129Xe MRI benefits from non-Cartesian acquisitions that sample k-space efficiently and rapidly. However, their reconstructions are complex and burdened by decay processes unique to hyperpolarized gas. Currently used gridded reconstructions are prone to artifacts caused by magnetization decay and are ill-suited for undersampling. We present a compressed sensing (CS) reconstruction approach that incorporates magnetization decay in the forward model, thereby producing images with increased sharpness and contrast, even in undersampled data.

METHODS

Radio-frequency, T1, andT 2 * $$ {\mathrm{T}}_2^{\ast } $$ decay processes were incorporated into the forward model and solved using iterative methods including CS. The decay-modeled reconstruction was validated in simulations and then tested in 2D/3D-spiral ventilation and 3D-radial gas-exchange MRI. Quantitative metrics including apparent-SNR and sharpness were compared between gridded, CS, and twofold undersampled CS reconstructions. Observations were validated in gas-exchange data collected from 15 healthy and 25 post-hematopoietic-stem-cell-transplant participants.

RESULTS

CS reconstructions in simulations yielded images with threefold increases in accuracy. CS increased sharpness and contrast for ventilation in vivo imaging and showed greater accuracy for undersampled acquisitions. CS improved gas-exchange imaging, particularly in the dissolved-phase where apparent-SNR improved, and structure was made discernable. Finally, CS showed repeatability in important global gas-exchange metrics including median dissolved-gas signal ratio and median angle between real/imaginary components.

CONCLUSION

A non-Cartesian CS reconstruction approach that incorporates hyperpolarized 129Xe decay processes is presented. This approach enables improved image sharpness, contrast, and overall image quality in addition to up-to threefold undersampling. This contribution benefits all hyperpolarized gas MRI through improved accuracy and decreased scan durations.

A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI

Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using regularizers to describe the images of interest. The reconstruction process is equivalent to solving a composite optimization problem. Accelerated proximal methods (APMs) are very popular approaches for such problems. This paper proposes a complex quasi-Newton proximal method (CQNPM) for the wavelet and total variation based CS MRI reconstruction. Compared with APMs, CQNPM requires fewer iterations to converge but needs to compute a more challenging proximal mapping called weighted proximal mapping (WPM). To make CQNPM more practical, we propose efficient methods to solve the related WPM. Numerical experiments on reconstructing non-Cartesian MRI data demonstrate the effectiveness and efficiency of CQNPM.

Radial magnetic resonance image reconstruction with a deep unrolled projected fast iterative soft-thresholding network

Radially sampling of magnetic resonance imaging (MRI) is an effective way to accelerate the imaging. How to preserve the image details in reconstruction is always challenging. In this work, a deep unrolled neural network is designed to emulate the iterative sparse image reconstruction process of a projected fast soft-threshold algorithm (pFISTA). The proposed method, an unrolled pFISTA network for Deep Radial MRI (pFISTA-DR), include the preprocessing module to refine coil sensitivity maps and initial reconstructed image, the learnable convolution filters to extract image feature maps, and adaptive threshold to robustly remove image artifacts. Experimental results show that, among the compared methods, pFISTA-DR provides the best reconstruction and achieved the highest PSNR, the highest SSIM and the lowest reconstruction errors.

Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models

Knowledge of the relative performance of the well-known sparse and low-rank compressed sensing models with 3D radial quantitative magnetic resonance imaging acquisitions is limited. We use 3D radial T1 relaxation time mapping data to compare the total variation, low-rank, and Huber penalty function approaches to regularization to provide insights into the relative performance of these image reconstruction models. Simulation and ex vivo specimen data were used to determine the best compressed sensing model as measured by normalized root mean squared error and structural similarity index. The large-scale compressed sensing models were solved by combining a GPU implementation of a preconditioned primal-dual proximal splitting algorithm to provide high-quality T1 maps within a feasible computation time. The model combining spatial total variation and locally low-rank regularization yielded the best performance, followed closely by the model combining spatial and contrast dimension total variation. Computation times ranged from 2 to 113 min, with the low-rank approaches taking the most time. The differences between the compressed sensing models are not necessarily large, but the overall performance is heavily dependent on the imaged object.

A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI

Radial sampling is a fast magnetic resonance imaging technique. Further imaging acceleration can be achieved with undersampling but how to reconstruct a clear image with fast algorithm is still challenging. Previous work has shown the advantage of removing undersampling image artifacts using the tight-frame sparse reconstruction model. This model was further solved with a projected fast iterative soft-thresholding algorithm (pFISTA). However, the convergence of this algorithm under radial sampling has not been clearly set up. In this work, the authors derived a theoretical convergence condition for this algorithm. This condition was approximated by estimating the maximal eigenvalue of reconstruction operators through the power iteration. Based on the condition, an optimal step size was further suggested to allow the fastest convergence. Verifications were made on the prospective in vivo data of static brain imaging and dynamic contrast-enhanced liver imaging, demonstrating that the recommended parameter allowed fast convergence in radial MRI.

Multicomponent MR fingerprinting reconstruction using joint-sparsity and low-rank constraints

PURPOSE

To develop an efficient algorithm for multicomponent MR fingerprinting (MC-MRF) reconstructions directly from highly undersampled data without making prior assumptions about tissue relaxation times and expected number of tissues.

METHODS

The proposed method reconstructs MC-MRF maps from highly undersampled data by iteratively applying a joint-sparsity constraint to the estimated tissue components. Intermediate component maps are obtained by a low-rank multicomponent alternating direction method of multipliers (MC-ADMM) including the non-negativity of tissue weights as an extra regularization term. Over iterations, the used dictionary compression is adjusted. The proposed method (k-SPIJN) is compared with a two-step approach in which image reconstruction and multicomponent estimations are performed sequentially and tested in numerical simulations and in vivo by applying different undersampling factors in eight healthy volunteers. In the latter case, fully sampled data serves as the reference.

RESULTS

The proposed method shows improved precision and accuracy in simulations compared with a state-of-art sequential approach. Obtained in vivo magnetization fraction maps for different tissue types show reduced systematic errors and reduced noise-like effects. Root mean square errors in estimated magnetization fraction maps significantly reduce from 13.0% <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>±</mml:mo></mml:mrow> <mml:annotation>$$ \pm $$</mml:annotation></mml:semantics> </mml:math> 5.8% with the conventional, two-step approach to 9.6% <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>±</mml:mo></mml:mrow> <mml:annotation>$$ \pm $$</mml:annotation></mml:semantics> </mml:math> 3.9% and 9.6% <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>±</mml:mo></mml:mrow> <mml:annotation>$$ \pm $$</mml:annotation></mml:semantics> </mml:math> 3.2% with the proposed MC-ADMM and k-SPIJN methods, respectively. Mean standard deviation in homogeneous white matter regions reduced significantly from 8.6% to 2.9% (two step vs. k-SPIJN).

CONCLUSION

The proposed MC-ADMM and k-SPIJN reconstruction methods estimate MC-MRF maps from highly undersampled data resulting in improved image quality compared with the existing method.

NC-PDNet: A Density-Compensated Unrolled Network for 2D and 3D Non-Cartesian MRI Reconstruction

Deep Learning has become a very promising avenue for magnetic resonance image (MRI) reconstruction. In this work, we explore the potential of unrolled networks for non-Cartesian acquisition settings. We design the NC-PDNet (Non-Cartesian Primal Dual Netwok), the first density-compensated (DCp) unrolled neural network, and validate the need for its key components via an ablation study. Moreover, we conduct some generalizability experiments to test this network in out-of-distribution settings, for example training on knee data and validating on brain data. The results show that NC-PDNet outperforms baseline (U-Net, Deep image prior) models both visually and quantitatively in all settings. In particular, in the 2D multi-coil acquisition scenario, the NC-PDNet provides up to a 1.2 dB improvement in peak signal-to-noise ratio (PSNR) over baseline networks, while also allowing a gain of at least 1dB in PSNR in generalization settings. We provide the open-source implementation of NC-PDNet, and in particular the Non-uniform Fourier Transform in TensorFlow, tested on 2D multi-coil and 3D single-coil k-space data.

Data-Consistent non-Cartesian deep subspace learning for efficient dynamic MR image reconstruction

Non-Cartesian sampling with subspace-constrained image reconstruction is a popular approach to dynamic MRI, but slow iterative reconstruction limits its clinical application. Data-consistent (DC) deep learning can accelerate reconstruction with good image quality, but has not been formulated for non-Cartesian subspace imaging. In this study, we propose a DC non-Cartesian deep subspace learning framework for fast, accurate dynamic MR image reconstruction. Four novel DC formulations are developed and evaluated: two gradient decent approaches, a directly solved approach, and a conjugate gradient approach. We applied a U-Net model with and without DC layers to reconstruct T1-weighted images for cardiac MR Multitasking (an advanced multidimensional imaging method), comparing our results to the iteratively reconstructed reference. Experimental results show that the proposed framework significantly improves reconstruction accuracy over the U-Net model without DC, while significantly accelerating the reconstruction over conventional iterative reconstruction.

Learning a preconditioner to accelerate compressed sensing reconstructions in MRI

Purpose

To learn a preconditioner that accelerates parallel imaging (PI) and compressed sensing (CS) reconstructions.

Methods

A convolutional neural network (CNN) with residual connections was used to train a preconditioning operator. Training and validation data were simulated using 50% brain images and 50% white Gaussian noise images. Each multichannel training example contains a simulated sampling mask, complex coil sensitivity maps, and two regularization parameter maps. The trained model was integrated in the preconditioned conjugate gradient (PCG) method as part of the split Bregman CS method. The acceleration performance was compared with that of a circulant PI‐CS preconditioner for varying undersampling factors, number of coil elements and anatomies.

Results

The learned preconditioner reduces the number of PCG iterations by a factor of 4, yielding a similar acceleration as an efficient circulant preconditioner. The method generalizes well to different sampling schemes, coil configurations and anatomies.

Conclusion

It is possible to learn adaptable preconditioners for PI and CS reconstructions that meet the performance of state‐of‐the‐art preconditioners. Further acceleration could be achieved by optimizing the network architecture and the training set. Such a preconditioner could also be integrated in fully learned reconstruction methods to accelerate the training process of unrolled networks.

Accelerating compressed sensing reconstruction of subsampled radial k-space data using geometrically-derived density compensation

Objective.To accelerate compressed sensing (CS) reconstruction of subsampled radial k-space data using a geometrically-derived density compensation function (gDCF) without significant loss in image quality.Approach.We developed a theoretical framework to calculate a gDCF based on Nyquist distance along the radial and circumferential directions of a discrete polar coordinate system. Our gDCF was compared against standard DCF (e.g. ramp filter) and another commonly used DCF (modified Shepp-Logan (SL) filter). The resulting image quality produced by each DCF was quantified using normalized root-mean-square-error (NRMSE), blur metric (1 = blurriest; 0 = sharpest), and structural similarity index (SSIM; 1 = perfect match; 0 = no match) compared with the reference. For filtered backprojection (FBP) of phantom data obtained at the Nyquist sampling rate, Cartesian k-space sampling was used as the reference. For CS reconstruction of subsampled cardiac magnetic resonance imaging datasets (real-time cardiac cine data with 11 projections per frame,n = 20 patients; cardiac perfusion data with 30 projections per frame,n = 19 patients), CS reconstruction without DCF was used as the reference.Main results.The NRMSE, SSIM, and blur metrics of the phantom data were good for all DCFs, confirming that our gDCF produces uniform densities at the upper limit (Nyquist). For CS reconstruction of subsampled real-time cine and cardiac perfusion datasets, the image quality metrics (SSIM, NRMSE) were significantly (p < 0.05) higher for our gDCF than other DCFs, and the reconstruction time was significantly (p < 0.05) faster for our gDCF (reference) than no DCF (11.9%-52.9% slower), standard DCF (23.9%-57.6% slower), and modified SL filter (13.5%-34.8% slower).Significance.The proposed gDCF accelerates CS reconstruction of subsampled radial k-space data without significant loss in image quality compared with no DCF as the reference.

Accelerated radial echo-planar spectroscopic imaging using golden angle view-ordering and compressed-sensing reconstruction with total variation regularization

PURPOSE

To implement a novel, accelerated, 2D radial echo-planar spectroscopic imaging (REPSI) sequence using undersampled radial k-space trajectories and compressed-sensing reconstruction, and to compare results with those from an undersampled Cartesian spectroscopic sequence.

METHODS

The REPSI sequence was implemented using golden-angle view-ordering on a 3T MRI scanner. Radial and Cartesian echo-planar spectroscopic imaging (EPSI) data were acquired at six acceleration factors, each with time-equivalent scan durations, and reconstructed using compressed sensing with total variation regularization. Results from prospectively and retrospectively undersampled phantom and in vivo brain data were compared over estimated concentrations and Cramer-Rao lower-bound values, normalized RMS errors of reconstructed metabolite maps, and percent absolute differences between fully sampled and reconstructed spectroscopic images.

RESULTS

The REPSI method with compressed sensing is able to tolerate greater reductions in scan time compared with EPSI. The reconstruction and quantitation metrics (i.e., spectral normalized RMS error maps, metabolite map normalized RMS error values [e.g., for total N-acetyl asparate, REPSI = 9.4% vs EPSI = 16.3%; acceleration factor = 2.5], percent absolute difference maps, and concentration and Cramer-Rao lower-bound estimates) showed that accelerated REPSI can reduce the scan time by a factor of 2.5 while retaining image and quantitation quality.

CONCLUSION

Accelerated MRSI using undersampled radial echo-planar acquisitions provides greater reconstruction accuracy and more reliable quantitation for a range of acceleration factors compared with time-equivalent compressed-sensing reconstructions of undersampled Cartesian EPSI. Compared to the Cartesian approach, radial undersampling with compressed sensing could help reduce 2D spectroscopic imaging acquisition time, and offers a better trade-off between imaging speed and quality.

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.

CG-SENSE revisited: Results from the first ISMRM reproducibility challenge

PURPOSE

The aim of this work is to shed light on the issue of reproducibility in MR image reconstruction in the context of a challenge. Participants had to recreate the results of "Advances in sensitivity encoding with arbitrary k-space trajectories" by Pruessmann et al. METHODS: The task of the challenge was to reconstruct radially acquired multicoil k-space data (brain/heart) following the method in the original paper, reproducing its key figures. Results were compared to consolidated reference implementations created after the challenge, accounting for the two most common programming languages used in the submissions (Matlab/Python).

RESULTS

Visually, differences between submissions were small. Pixel-wise differences originated from image orientation, assumed field-of-view, or resolution. The reference implementations were in good agreement, both visually and in terms of image similarity metrics.

DISCUSSION AND CONCLUSION

While the description level of the published algorithm enabled participants to reproduce CG-SENSE in general, details of the implementation varied, for example, density compensation or Tikhonov regularization. Implicit assumptions about the data lead to further differences, emphasizing the importance of sufficient metadata accompanying open datasets. Defining reproducibility quantitatively turned out to be nontrivial for this image reconstruction challenge, in the absence of ground-truth results. Typical similarity measures like NMSE of SSIM were misled by image intensity scaling and outlier pixels. Thus, to facilitate reproducibility, researchers are encouraged to publish code and data alongside the original paper. Future methodological papers on MR image reconstruction might benefit from the consolidated reference implementations of CG-SENSE presented here, as a benchmark for methods comparison.