Fast iterative algorithm for the reconstruction of multishot non-cartesian diffusion data

Deep learning initialized compressed sensing (Deli-CS) in volumetric spatio-temporal subspace reconstruction

OBJECT

Spatio-temporal MRI methods offer rapid whole-brain multi-parametric mapping, yet they are often hindered by prolonged reconstruction times or prohibitively burdensome hardware requirements. The aim of this project is to reduce reconstruction time using deep learning.

MATERIALS AND METHODS

This study focuses on accelerating the reconstruction of volumetric multi-axis spiral projection MRF, aiming for whole-brain T1 and T2 mapping, while ensuring a streamlined approach compatible with clinical requirements. To optimize reconstruction time, the traditional method is first revamped with a memory-efficient GPU implementation. Deep Learning Initialized Compressed Sensing (Deli-CS) is then introduced, which initiates iterative reconstruction with a DL-generated seed point, reducing the number of iterations needed for convergence.

RESULTS

The full reconstruction process for volumetric multi-axis spiral projection MRF is completed in just 20 min compared to over 2 h for the previously published implementation. Comparative analysis demonstrates Deli-CS's efficiency in expediting iterative reconstruction while maintaining high-quality results.

DISCUSSION

By offering a rapid warm start to the iterative reconstruction algorithm, this method substantially reduces processing time while preserving reconstruction quality. Its successful implementation paves the way for advanced spatio-temporal MRI techniques, addressing the challenge of extensive reconstruction times and ensuring efficient, high-quality imaging in a streamlined manner.

Self-supervised learning for improved calibrationless radial MRI with NLINV-Net

PURPOSE

To develop a neural network architecture for improved calibrationless reconstruction of radial data when no ground truth is available for training.

METHODS

NLINV-Net is a model-based neural network architecture that directly estimates images and coil sensitivities from (radial) k-space data via nonlinear inversion (NLINV). Combined with a training strategy using self-supervision via data undersampling (SSDU), it can be used for imaging problems where no ground truth reconstructions are available. We validated the method for (1) real-time cardiac imaging and (2) single-shot subspace-based quantitative T1 mapping. Furthermore, region-optimized virtual (ROVir) coils were used to suppress artifacts stemming from outside the field of view and to focus the k-space-based SSDU loss on the region of interest. NLINV-Net-based reconstructions were compared with conventional NLINV and PI-CS (parallel imaging + compressed sensing) reconstruction and the effect of the region-optimized virtual coils and the type of training loss was evaluated qualitatively.

RESULTS

NLINV-Net-based reconstructions contain significantly less noise than the NLINV-based counterpart. ROVir coils effectively suppress streakings which are not suppressed by the neural networks while the ROVir-based focused loss leads to visually sharper time series for the movement of the myocardial wall in cardiac real-time imaging. For quantitative imaging, T1-maps reconstructed using NLINV-Net show similar quality as PI-CS reconstructions, but NLINV-Net does not require slice-specific tuning of the regularization parameter.

CONCLUSION

NLINV-Net is a versatile tool for calibrationless imaging which can be used in challenging imaging scenarios where a ground truth is not available.

Deep Learning Initialized Compressed Sensing (Deli-CS) in Volumetric Spatio-Temporal Subspace Reconstruction

Introduction

Spatio-temporal MRI methods enable whole-brain multi-parametric mapping at ultra-fast acquisition times through efficient k-space encoding, but can have very long reconstruction times, which limit their integration into clinical practice. Deep learning (DL) is a promising approach to accelerate reconstruction, but can be computationally intensive to train and deploy due to the large dimensionality of spatio-temporal MRI. DL methods also need large training data sets and can produce results that don't match the acquired data if data consistency is not enforced. The aim of this project is to reduce reconstruction time using DL whilst simultaneously limiting the risk of deep learning induced hallucinations, all with modest hardware requirements.

Methods

Deep Learning Initialized Compressed Sensing (Deli-CS) is proposed to reduce the reconstruction time of iterative reconstructions by "kick-starting" the iterative reconstruction with a DL generated starting point. The proposed framework is applied to volumetric multi-axis spiral projection MRF that achieves whole-brain T1 and T2 mapping at 1-mm isotropic resolution for a 2-minute acquisition. First, the traditional reconstruction is optimized from over two hours to less than 40 minutes while using more than 90% less RAM and only 4.7 GB GPU memory, by using a memory-efficient GPU implementation. The Deli-CS framework is then implemented and evaluated against the above reconstruction.

Results

Deli-CS achieves comparable reconstruction quality with 50% fewer iterations bringing the full reconstruction time to 20 minutes.

Conclusion

Deli-CS reduces the reconstruction time of subspace reconstruction of volumetric spatio-temporal acquisitions by providing a warm start to the iterative reconstruction algorithm.

Free-running 3D whole-heart T1 and T2 mapping and cine MRI using low-rank reconstruction with non-rigid cardiac motion correction

PURPOSE

To introduce non-rigid cardiac motion correction into a novel free-running framework for the simultaneous acquisition of 3D whole-heart myocardial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_1 $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_2 $$</mml:annotation></mml:semantics> </mml:math> maps and cine images, enabling a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>∼</mml:mo></mml:mrow> <mml:annotation>$$ \sim $$</mml:annotation></mml:semantics> </mml:math> 3-min scan.

METHODS

Data were acquired using a free-running 3D golden-angle radial readout interleaved with inversion recovery and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_2 $$</mml:annotation></mml:semantics> </mml:math> -preparation pulses. After correction for translational respiratory motion, non-rigid cardiac-motion-corrected reconstruction with dictionary-based low-rank compression and patch-based regularization enabled 3D whole-heart <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_1 $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_2 $$</mml:annotation></mml:semantics> </mml:math> mapping at any given cardiac phase as well as whole-heart cardiac cine imaging. The framework was validated and compared with established methods in 11 healthy subjects.

RESULTS

Good quality 3D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_1 $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_2 $$</mml:annotation></mml:semantics> </mml:math> maps and cine images were reconstructed for all subjects. Septal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_1 $$</mml:annotation></mml:semantics> </mml:math> values using the proposed approach ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>1200</mml:mn> <mml:mo>±</mml:mo> <mml:mn>50</mml:mn></mml:mrow> <mml:annotation>$$ 1200\pm 50 $$</mml:annotation></mml:semantics> </mml:math> ms) were higher than those from a 2D MOLLI sequence ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>1063</mml:mn> <mml:mo>±</mml:mo> <mml:mn>33</mml:mn></mml:mrow> <mml:annotation>$$ 1063\pm 33 $$</mml:annotation></mml:semantics> </mml:math> ms), which is known to underestimate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_1 $$</mml:annotation></mml:semantics> </mml:math> , while <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_2 $$</mml:annotation></mml:semantics> </mml:math> values from the proposed approach ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>51</mml:mn> <mml:mo>±</mml:mo> <mml:mn>4</mml:mn></mml:mrow> <mml:annotation>$$ 51\pm 4 $$</mml:annotation></mml:semantics> </mml:math> ms) were in good agreement with those from a 2D GraSE sequence ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>51</mml:mn> <mml:mo>±</mml:mo> <mml:mn>2</mml:mn></mml:mrow> <mml:annotation>$$ 51\pm 2 $$</mml:annotation></mml:semantics> </mml:math> ms).

CONCLUSION

The proposed technique provides 3D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_1 $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {T}_2 $$</mml:annotation></mml:semantics> </mml:math> maps and cine images with isotropic spatial resolution in a single <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mo>∼</mml:mo></mml:mrow> <mml:annotation>$$ \sim $$</mml:annotation></mml:semantics> </mml:math> 3.3-min scan.

Myocardial T1, T2, T2*, and fat fraction quantification via low-rank motion-corrected cardiac MR fingerprinting

Purpose

Develop a novel 2D cardiac MR fingerprinting (MRF) approach to enable simultaneous T1, T2, T2*, and fat fraction (FF) myocardial tissue characterization in a single breath‐hold scan.

Methods

Simultaneous, co‐registered, multi‐parametric mapping of T1, T2, and FF has been recently achieved with cardiac MRF. Here, we further incorporate T2* quantification within this approach, enabling simultaneous T1, T2, T2*, and FF myocardial tissue characterization in a single breath‐hold scan. T2* quantification is achieved with an eight‐echo readout that requires a long cardiac acquisition window. A novel low‐rank motion‐corrected (LRMC) reconstruction is exploited to correct for cardiac motion within the long acquisition window. The proposed T1/T2/T2*/FF cardiac MRF was evaluated in phantom and in 10 healthy subjects in comparison to conventional mapping techniques.

Results

The proposed approach achieved high quality parametric mapping of T1, T2, T2*, and FF with corresponding normalized RMS error (RMSE) T1 = 5.9%, T2 = 9.6% (T2 values <100 ms), T2* = 3.3% (T2* values <100 ms), and FF = 0.8% observed in phantom scans. In vivo, the proposed approach produced higher left‐ventricular myocardial T1 values than MOLLI (1148 vs 1056 ms), lower T2 values than T2‐GraSE (42.8 vs 50.6 ms), lower T2* values than eight‐echo gradient echo (GRE) (35.0 vs 39.4 ms), and higher FF values than six‐echo GRE (0.8 vs 0.3 %) reference techniques. The proposed approach achieved considerable reduction in motion artifacts compared to cardiac MRF without motion correction, improved spatial uniformity, and statistically higher apparent precision relative to conventional mapping for all parameters.

Conclusion

The proposed cardiac MRF approach enables simultaneous, co‐registered mapping of T1, T2, T2*, and FF in a single breath‐hold for comprehensive myocardial tissue characterization, achieving higher apparent precision than conventional methods.

Physics-based reconstruction methods for magnetic resonance imaging

Conventional magnetic resonance imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions explicitly model the physical laws that govern the MRI signal generation. By formulating image reconstruction as an inverse problem, quantitative maps of the underlying physical parameters can then be extracted directly from efficiently acquired k-space signals without intermediate image reconstruction-addressing both shortcomings of conventional MRI at the same time. This review will discuss basic concepts of model-based reconstructions and report on our experience in developing several model-based methods over the last decade using selected examples that are provided complete with data and code. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Model-based reconstruction for simultaneous multi-slice T1 mapping using single-shot inversion-recovery radial FLASH

PURPOSE

To develop a single-shot multi-slice T 1 mapping method by combing simultaneous multi-slice (SMS) excitations, single-shot inversion-recovery (IR) radial fast low-angle shot (FLASH), and a nonlinear model-based reconstruction method.

METHODS

SMS excitations are combined with a single-shot IR radial FLASH sequence for data acquisition. A previously developed single-slice calibrationless model-based reconstruction is extended to SMS, formulating the estimation of parameter maps and coil sensitivities from all slices as a single nonlinear inverse problem. Joint-sparsity constraints are further applied to the parameter maps to improve T 1 precision. Validations of the proposed method are performed for a phantom and for the human brain and liver in 6 healthy adult subjects.

RESULTS

Phantom results confirm good T 1 accuracy and precision of the simultaneously acquired multi-slice T 1 maps in comparison to single-slice references. In vivo human brain studies demonstrate the better performance of SMS acquisitions compared to the conventional spoke-interleaved multi-slice acquisition using model-based reconstruction. Aside from good accuracy and precision, the results of 6 healthy subjects in both brain and abdominal studies confirm good repeatability between scan and re-scans. The proposed method can simultaneously acquire T 1 maps for 5 slices of a human brain ( 0.75 × 0.75 × 5 mm 3 ) or 3 slices of the abdomen ( 1.25 × 1.25 × 6 mm 3 ) within 4 seconds.

CONCLUSIONS

The IR SMS radial FLASH acquisition together with a nonlinear model-based reconstruction enable rapid high-resolution multi-slice T 1 mapping with good accuracy, precision, and repeatability.

Frequency-modulated SSFP with radial sampling and subspace reconstruction: A time-efficient alternative to phase-cycled bSSFP

PURPOSE

A novel subspace-based reconstruction method for frequency-modulated balanced steady-state free precession (fmSSFP) MRI is presented. In this work, suitable data acquisition schemes, subspace sizes, and efficiencies for banding removal are investigated.

THEORY AND METHODS

By combining a fmSSFP MRI sequence with a 3D stack-of-stars trajectory, scan efficiency is maximized as spectral information is obtained without intermediate preparation phases. A memory-efficient reconstruction routine is implemented by introducing the low-frequency Fourier transform as a subspace which allows for the formulation of a convex reconstruction problem. The removal of banding artifacts is investigated by comparing the proposed acquisition and reconstruction technique to phase-cycled bSSFP MRI. Aliasing properties of different undersampling schemes are analyzed and water/fat separation is demonstrated by reweighting the reconstructed subspace coefficients to generate virtual spectral responses in a post-processing step.

RESULTS

A simple root-of-sum-of-squares combination of the reconstructed subspace coefficients yields high-SNR images with the characteristic bSSFP contrast but without banding artifacts. Compared to Golden-Angle trajectories, turn-based sampling schemes were superior in minimizing aliasing across reconstructed subspace coefficients. Water/fat separated images of the human knee were obtained by reweighting subspace coefficients.

CONCLUSIONS

The novel subspace-based fmSSFP MRI technique emerges as a time-efficient alternative to phase-cycled bSFFP. The method does not need intermediate preparation phases, offers high SNR and avoids banding artifacts. Reweighting of the reconstructed subspace coefficients allows for generating virtual spectral responses with applications to water/fat separation.

Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH

PURPOSE

To develop a model-based reconstruction technique for single-shot T₁ mapping with high spatial resolution, accuracy, and precision using an inversion-recovery (IR) fast low-angle shot (FLASH) acquisition with radial encoding.

METHODS

The proposed model-based reconstruction jointly estimates all model parameters, that is, the equilibrium magnetization, steady-state magnetization, 1/ T1*, and all coil sensitivities from the data of a single-shot IR FLASH acquisition with a small golden-angle radial trajectory. Joint sparsity constraints on the parameter maps are exploited to improve the performance of the iteratively regularized Gauss-Newton method chosen for solving the nonlinear inverse problem. Validations include both a numerical and experimental T₁ phantom, as well as in vivo studies of the human brain and liver at 3 T.

RESULTS

In comparison to previous reconstruction methods for single-shot T₁ mapping, which are based on real-time MRI with pixel-wise fitting and a model-based approach with a predetermination of coil sensitivities, the proposed method presents with improved robustness against phase errors and numerical precision in both phantom and in vivo studies.

CONCLUSION

The comprehensive model-based reconstruction with L1 regularization offers rapid and robust T₁ mapping with high accuracy and precision. The method warrants accelerated computing and online implementation for extended clinical trials. Magn Reson Med 79:730-740, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

T2 shuffling: Sharp, multicontrast, volumetric fast spin-echo imaging

PURPOSE

A new acquisition and reconstruction method called T2 Shuffling is presented for volumetric fast spin-echo (three-dimensional [3D] FSE) imaging. T2 Shuffling reduces blurring and recovers many images at multiple T2 contrasts from a single acquisition at clinically feasible scan times (6-7 min).

THEORY AND METHODS

The parallel imaging forward model is modified to account for temporal signal relaxation during the echo train. Scan efficiency is improved by acquiring data during the transient signal decay and by increasing echo train lengths without loss in signal-to-noise ratio (SNR). By (1) randomly shuffling the phase encode view ordering, (2) constraining the temporal signal evolution to a low-dimensional subspace, and (3) promoting spatio-temporal correlations through locally low rank regularization, a time series of virtual echo time images is recovered from a single scan. A convex formulation is presented that is robust to partial voluming and radiofrequency field inhomogeneity.

RESULTS

Retrospective undersampling and in vivo scans confirm the increase in sharpness afforded by T2 Shuffling. Multiple image contrasts are recovered and used to highlight pathology in pediatric patients. A proof-of-principle method is integrated into a clinical musculoskeletal imaging workflow.

CONCLUSION

The proposed T2 Shuffling method improves the diagnostic utility of 3D FSE by reducing blurring and producing multiple image contrasts from a single scan. Magn Reson Med 77:180-195, 2017. © 2016 Wiley Periodicals, Inc.