Parallel imaging with nonlinear reconstruction using variational penalties

Accelerated MRI reconstructions via variational network and feature domain learning

We introduce three architecture modifications to enhance the performance of the end-to-end (E2E) variational network (VarNet) for undersampled MRI reconstructions. We first implemented the Feature VarNet, which propagates information throughout the cascades of the network in an N-channel feature-space instead of a 2-channel feature-space. Then, we add an attention layer that utilizes the spatial locations of Cartesian undersampling artifacts to further improve performance. Lastly, we combined the Feature and E2E VarNets into the Feature-Image (FI) VarNet, to facilitate cross-domain learning and boost accuracy. Reconstructions were evaluated on the fastMRI dataset using standard metrics and clinical scoring by three neuroradiologists. Feature and FI VarNets outperformed the E2E VarNet for 4 × , 5 × and 8 × Cartesian undersampling in all studied metrics. FI VarNet secured second place in the public fastMRI leaderboard for 4 × Cartesian undersampling, outperforming all open-source models in the leaderboard. Radiologists rated FI VarNet brain reconstructions with higher quality and sharpness than the E2E VarNet reconstructions. FI VarNet excelled in preserving anatomical details, including blood vessels, whereas E2E VarNet discarded or blurred them in some cases. The proposed FI VarNet enhances the reconstruction quality of undersampled MRI and could enable clinically acceptable reconstructions at higher acceleration factors than currently possible.

On retrospective k-space subsampling schemes for deep MRI reconstruction

Acquiring fully-sampled MRI k-space data is time-consuming, and collecting accelerated data can reduce the acquisition time. Employing 2D Cartesian-rectilinear subsampling schemes is a conventional approach for accelerated acquisitions; however, this often results in imprecise reconstructions, even with the use of Deep Learning (DL), especially at high acceleration factors. Non-rectilinear or non-Cartesian trajectories can be implemented in MRI scanners as alternative subsampling options. This work investigates the impact of the k-space subsampling scheme on the quality of reconstructed accelerated MRI measurements produced by trained DL models. The Recurrent Variational Network (RecurrentVarNet) was used as the DL-based MRI-reconstruction architecture. Cartesian, fully-sampled multi-coil k-space measurements from three datasets were retrospectively subsampled with different accelerations using eight distinct subsampling schemes: four Cartesian-rectilinear, two Cartesian non-rectilinear, and two non-Cartesian. Experiments were conducted in two frameworks: scheme-specific, where a distinct model was trained and evaluated for each dataset-subsampling scheme pair, and multi-scheme, where for each dataset a single model was trained on data randomly subsampled by any of the eight schemes and evaluated on data subsampled by all schemes. In both frameworks, RecurrentVarNets trained and evaluated on non-rectilinearly subsampled data demonstrated superior performance, particularly for high accelerations. In the multi-scheme setting, reconstruction performance on rectilinearly subsampled data improved when compared to the scheme-specific experiments. Our findings demonstrate the potential for using DL-based methods, trained on non-rectilinearly subsampled measurements, to optimize scan time and image quality.

Equilibrated Zeroth-Order Unrolled Deep Network for Parallel MR Imaging

In recent times, model-driven deep learning has evolved an iterative algorithm into a cascade network by replacing the regularizer's first-order information, such as the (sub)gradient or proximal operator, with a network module. This approach offers greater explainability and predictability compared to typical data-driven networks. However, in theory, there is no assurance that a functional regularizer exists whose first-order information matches the substituted network module. This implies that the unrolled network output may not align with the regularization models. Furthermore, there are few established theories that guarantee global convergence and robustness (regularity) of unrolled networks under practical assumptions. To address this gap, we propose a safeguarded methodology for network unrolling. Specifically, for parallel MR imaging, we unroll a zeroth-order algorithm, where the network module serves as a regularizer itself, allowing the network output to be covered by a regularization model. Additionally, inspired by deep equilibrium models, we conduct the unrolled network before backpropagation to converge to a fixed point and then demonstrate that it can tightly approximate the actual MR image. We also prove that the proposed network is robust against noisy interferences if the measurement data contain noise. Finally, numerical experiments indicate that the proposed network consistently outperforms state-of-the-art MRI reconstruction methods, including traditional regularization and unrolled deep learning techniques.

Stable Deep MRI Reconstruction Using Generative Priors

Data-driven approaches recently achieved remarkable success in magnetic resonance imaging (MRI) reconstruction, but integration into clinical routine remains challenging due to a lack of generalizability and interpretability. In this paper, we address these challenges in a unified framework based on generative image priors. We propose a novel deep neural network based regularizer which is trained in a generative setting on reference magnitude images only. After training, the regularizer encodes higher-level domain statistics which we demonstrate by synthesizing images without data. Embedding the trained model in a classical variational approach yields high-quality reconstructions irrespective of the sub-sampling pattern. In addition, the model shows stable behavior when confronted with out-of-distribution data in the form of contrast variation. Furthermore, a probabilistic interpretation provides a distribution of reconstructions and hence allows uncertainty quantification. To reconstruct parallel MRI, we propose a fast algorithm to jointly estimate the image and the sensitivity maps. The results demonstrate competitive performance, on par with state-of-the-art end-to-end deep learning methods, while preserving the flexibility with respect to sub-sampling patterns and allowing for uncertainty quantification.

Balanced Steady-State Free Precession Cine MR Imaging in the Presence of Cardiac Devices: Value of Interleaved Radial Linear Combination Acquisition With Partial Dephasing

BACKGROUND

Balanced steady-state free precession (bSSFP) is important in cardiac MRI but suffers from off-resonance artifacts. The interpretation-limiting artifacts in patients with cardiac implants remain an unsolved issue.

PURPOSE

To develop an interleaved radial linear combination bSSFP (lcSSFP) method with partial dephasing (PD) for improved cardiac cine imaging when implanted cardiovascular devices are present.

STUDY TYPE

Prospective.

PHANTOM AND SUBJECTS

Flow phantom adjacent to a pacemaker and 10 healthy volunteers (mean age ± standard deviation: 31.9 ± 2.9 years, 4 females) with a cardioverter-defibrillator (ICD) positioned extracorporeally at the left chest in the prepectoral region.

FIELD STRENGTH/SEQUENCE

A 3-T, 1) Cartesian bSSFP, 2) Cartesian gradient echo (GRE), 3) Cartesian lcSSFP, and 4) radial lcSSFP cine sequences.

ASSESSMENT

Flow artifacts mitigation using PD was validated with phantom experiments. Undersampled radial lcSSFP with interleaving across phase-cyclings and cardiac phases (RLC-SSFP), combined with PD, was then employed for achieving improved quality of cine images from left ventricular short-axis view. The image quality in the presence of cardiac devices was qualitatively assessed by three independent raters (1 = worst, 5 = best), regarding five criteria (banding artifacts, streak artifacts, flow artifacts, cavity visibility, and overall image quality).

STATISTICAL TESTS

Wilcoxon rank-sum test for the five criteria between Cartesian bSSFP cine and RLC-SSFP with PD. Fleiss kappa test for inter-reader agreement. A P value < 0.05 was considered statistically significant.

RESULTS

Based on simulations and phantom experiments, 60 projections per phase cycling and 1/6 PD were chosen. The in vivo experiments demonstrated significantly reduced banding artifacts (4.8 ± 0.4 vs. 2.7 ± 0.7), fewer streak artifacts (3.7 ± 0.6 vs. 2.6 ± 0.7) and flow artifacts (4.4 ± 0.4 vs. 3.7 ± 0.6), therefore improved cavity visibility (4.1 ± 0.4 vs. 2.9 ± 0.9) and overall quality (4.0 ± 0.4 vs. 2.7 ± 0.7).

DATA CONCLUSION

RLC-SSFP method with PD may improve cine image quality in subjects with cardiac devices.

EVIDENCE LEVEL

2.

TECHNICAL EFFICACY

Stage 1.

JSENSE-Pro: Joint sensitivity estimation and image reconstruction in parallel imaging using pre-learned subspaces of coil sensitivity functions

PURPOSE

To improve calibrationless parallel imaging using pre-learned subspaces of coil sensitivity functions.

THEORY AND METHODS

A subspace-based joint sensitivity estimation and image reconstruction method was developed for improved parallel imaging with no calibration data. Specifically, we proposed to use a probabilistic subspace model to capture prior information of the coil sensitivity functions from previous scans acquired using the same receiver system. Both the subspace basis and coefficient distributions were learned from a small set of training data. The learned subspace model was then incorporated into the regularized reconstruction formalism that includes a sparsity prior. The nonlinear optimization problem was solved using alternating minimization algorithm. Public fastMRI brain dataset was retrospectively undersampled by different schemes for performance evaluation of the proposed method.

RESULTS

With no calibration data, the proposed method consistently produced the most accurate coil sensitivity estimation and highest quality image reconstructions at all acceleration factors tested in comparison with state-of-the-art methods including JSENSE, DeepSENSE, P-LORAKS, and Sparse BLIP. Our results are comparable to or even better than those from SparseSENSE, which used calibration data for sensitivity estimation. The work also demonstrated that the probabilistic subspace model learned from T₂ w data can be generalized to aiding the reconstruction of FLAIR data acquired from the same receiver system.

CONCLUSION

A subspace-based method named JSENSE-Pro has been proposed for accelerated parallel imaging without the acquisition of companion calibration data. The method is expected to further enhance the practical utility of parallel imaging, especially in applications where calibration data acquisition is not desirable or limited.

Stabilizing deep tomographic reconstruction: Part A. Hybrid framework and experimental results

A recent PNAS paper reveals that several popular deep reconstruction networks are unstable. Specifically, three kinds of instabilities were reported: (1) strong image artefacts from tiny perturbations, (2) small features missed in a deeply reconstructed image, and (3) decreased imaging performance with increased input data. Here, we propose an analytic compressed iterative deep (ACID) framework to address this challenge. ACID synergizes a deep network trained on big data, kernel awareness from compressed sensing (CS)-inspired processing, and iterative refinement to minimize the data residual relative to real measurement. Our study demonstrates that the ACID reconstruction is accurate, is stable, and sheds light on the converging mechanism of the ACID iteration under a bounded relative error norm assumption. ACID not only stabilizes an unstable deep reconstruction network but also is resilient against adversarial attacks to the whole ACID workflow, being superior to classic sparsity-regularized reconstruction and eliminating the three kinds of instabilities.

End-to-End Deep Learning of Non-rigid Groupwise Registration and Reconstruction of Dynamic MRI

Temporal correlation has been exploited for accelerated dynamic MRI reconstruction. Some methods have modeled inter-frame motion into the reconstruction process to produce temporally aligned image series and higher reconstruction quality. However, traditional motion-compensated approaches requiring iterative optimization of registration and reconstruction are time-consuming, while most deep learning-based methods neglect motion in the reconstruction process. We propose an unrolled deep learning framework with each iteration consisting of a groupwise diffeomorphic registration network (GRN) and a motion-augmented reconstruction network. Specifically, the whole dynamic sequence is registered at once to an implicit template which is used to generate a new set of dynamic images to efficiently exploit the full temporal information of the acquired data via the GRN. The generated dynamic sequence is then incorporated into the reconstruction network to augment the reconstruction performance. The registration and reconstruction networks are optimized in an end-to-end fashion for simultaneous motion estimation and reconstruction of dynamic images. The effectiveness of the proposed method is validated in highly accelerated cardiac cine MRI by comparing with other state-of-the-art approaches.

Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.

Systematic evaluation of iterative deep neural networks for fast parallel MRI reconstruction with sensitivity-weighted coil combination

PURPOSE

To systematically investigate the influence of various data consistency layers and regularization networks with respect to variations in the training and test data domain, for sensitivity-encoded accelerated parallel MR image reconstruction.

THEORY AND METHODS

Magnetic resonance (MR) image reconstruction is formulated as a learned unrolled optimization scheme with a down-up network as regularization and varying data consistency layers. The proposed networks are compared to other state-of-the-art approaches on the publicly available fastMRI knee and neuro dataset and tested for stability across different training configurations regarding anatomy and number of training samples.

RESULTS

Data consistency layers and expressive regularization networks, such as the proposed down-up networks, form the cornerstone for robust MR image reconstruction. Physics-based reconstruction networks outperform post-processing methods substantially for R = 4 in all cases and for R = 8 when the training and test data are aligned. At R = 8, aligning training and test data is more important than architectural choices.

CONCLUSION

In this work, we study how dataset sizes affect single-anatomy and cross-anatomy training of neural networks for MRI reconstruction. The study provides insights into the robustness, properties, and acceleration limits of state-of-the-art networks, and our proposed down-up networks. These key insights provide essential aspects to successfully translate learning-based MRI reconstruction to clinical practice, where we are confronted with limited datasets and various imaged anatomies.

Maxwell parallel imaging

PURPOSE

To develop a general framework for parallel imaging (PI) with the use of Maxwell regularization for the estimation of the sensitivity maps (SMs) and constrained optimization for the parameter-free image reconstruction.

THEORY AND METHODS

Certain characteristics of both the SMs and the images are routinely used to regularize the otherwise ill-posed optimization-based joint reconstruction from highly accelerated PI data. In this paper, we rely on a fundamental property of SMs-they are solutions of Maxwell equations-we construct the subspace of all possible SM distributions supported in a given field-of-view, and we promote solutions of SMs that belong in this subspace. In addition, we propose a constrained optimization scheme for the image reconstruction, as a second step, once an accurate estimation of the SMs is available. The resulting method, dubbed Maxwell parallel imaging (MPI), works for both 2D and 3D, with Cartesian and radial trajectories, and minimal calibration signals.

RESULTS

The effectiveness of MPI is illustrated for various undersampling schemes, including radial, variable-density Poisson-disc, and Cartesian, and is compared against the state-of-the-art PI methods. Finally, we include some numerical experiments that demonstrate the memory footprint reduction of the constructed Maxwell basis with the help of tensor decomposition, thus allowing the use of MPI for full 3D image reconstructions.

CONCLUSION

The MPI framework provides a physics-inspired optimization method for the accurate and efficient image reconstruction from arbitrary accelerated scans.

Dynamic MRI reconstruction with end-to-end motion-guided network

Temporal correlation in dynamic magnetic resonance imaging (MRI), such as cardiac MRI, is informative and important to understand motion mechanisms of body regions. Modeling such information into the MRI reconstruction process produces temporally coherent image sequence and reduces imaging artifacts and blurring. However, existing deep learning based approaches neglect motion information during the reconstruction procedure, while traditional motion-guided methods are hindered by heuristic parameter tuning and long inference time. We propose a novel dynamic MRI reconstruction approach called MODRN and an end-to-end improved version called MODRN(e2e), both of which enhance the reconstruction quality by infusing motion information into the modeling process with deep neural networks. The central idea is to decompose the motion-guided optimization problem of dynamic MRI reconstruction into three components: Dynamic Reconstruction Network, Motion Estimation and Motion Compensation. Extensive experiments have demonstrated the effectiveness of our proposed approach compared to other state-of-the-art approaches.

A publicly available virtual cohort of four-chamber heart meshes for cardiac electro-mechanics simulations

Computational models of the heart are increasingly being used in the development of devices, patient diagnosis and therapy guidance. While software techniques have been developed for simulating single hearts, there remain significant challenges in simulating cohorts of virtual hearts from multiple patients. To facilitate the development of new simulation and model analysis techniques by groups without direct access to medical data, image analysis techniques and meshing tools, we have created the first publicly available virtual cohort of twenty-four four-chamber hearts. Our cohort was built from heart failure patients, age 67±14 years. We segmented four-chamber heart geometries from end-diastolic (ED) CT images and generated linear tetrahedral meshes with an average edge length of 1.1±0.2mm. Ventricular fibres were added in the ventricles with a rule-based method with an orientation of -60° and 80° at the epicardium and endocardium, respectively. We additionally refined the meshes to an average edge length of 0.39±0.10mm to show that all given meshes can be resampled to achieve an arbitrary desired resolution. We ran simulations for ventricular electrical activation and free mechanical contraction on all 1.1mm-resolution meshes to ensure that our meshes are suitable for electro-mechanical simulations. Simulations for electrical activation resulted in a total activation time of 149±16ms. Free mechanical contractions gave an average left ventricular (LV) and right ventricular (RV) ejection fraction (EF) of 35±1% and 30±2%, respectively, and a LV and RV stroke volume (SV) of 95±28mL and 65±11mL, respectively. By making the cohort publicly available, we hope to facilitate large cohort computational studies and to promote the development of cardiac computational electro-mechanics for clinical applications.

Deep-Learning Methods for Parallel Magnetic Resonance Imaging Reconstruction: A Survey of the Current Approaches, Trends, and Issues

Following the success of deep learning in a wide range of applications, neural network-based machine learning techniques have received interest as a means of accelerating magnetic resonance imaging (MRI). A number of ideas inspired by deep learning techniques from computer vision and image processing have been successfully applied to non-linear image reconstruction in the spirit of compressed sensing for both low dose computed tomography and accelerated MRI. The additional integration of multi-coil information to recover missing k-space lines in the MRI reconstruction process, is still studied less frequently, even though it is the de-facto standard for currently used accelerated MR acquisitions. This manuscript provides an overview of the recent machine learning approaches that have been proposed specifically for improving parallel imaging. A general background introduction to parallel MRI is given that is structured around the classical view of image space and k-space based methods. Both linear and non-linear methods are covered, followed by a discussion of recent efforts to further improve parallel imaging using machine learning, and specifically using artificial neural networks. Image-domain based techniques that introduce improved regularizers are covered as well as k-space based methods, where the focus is on better interpolation strategies using neural networks. Issues and open problems are discussed as well as recent efforts for producing open datasets and benchmarks for the community.

Motion Compensated Dynamic MRI Reconstruction With Local Affine Optical Flow Estimation

This paper proposes a novel framework to reconstruct dynamic magnetic resonance imaging (DMRI) with motion compensation (MC). Specifically, by combining the intensity-based optical flow constraint with the traditional compressed sensing scheme, we are able to jointly reconstruct the DMRI sequences and estimate the interframe motion vectors. Then, the DMRI reconstruction can be refined through MC with the estimated motion field. By employing the coarse-to-fine multi-scale resolution strategy, we are able to update the motion field in different spatial scales. The estimated motion vectors need to be interpolated to the finest resolution scale to compensate the DMRI reconstruction. Moreover, the proposed framework is capable of handling a wide class of prior information (regularizations) for DMRI reconstruction, such as sparsity, low rank, and total variation. The formulated optimization problem is solved by a primal-dual algorithm with linesearch due to its efficiency when dealing with non-differentiable problems. Experiments on various DMRI datasets validate the reconstruction quality improvement using the proposed scheme in comparison to several state-of-the-art algorithms.

A Generalized Structured Low-Rank Matrix Completion Algorithm for MR Image Recovery

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their undersampled Fourier coefficients using infimal convolution regularizations. The image is modeled as the superposition of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low-rank property of the matrices to formulate a combined regularized optimization problem. In order to solve the problem efficiently and to avoid the high-memory demand resulting from the large-scale Toeplitz matrices, we introduce a fast and a memory-efficient algorithm based on the half-circulant approximation of the Toeplitz matrix. We demonstrate our algorithm in the context of single and multi-channel MR images recovery. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the state-of-the-art approaches.

Compressed sensing MRI: a review from signal processing perspective

Magnetic resonance imaging (MRI) is an inherently slow imaging modality, since it acquires multi-dimensional k-space data through 1-D free induction decay or echo signals. This often limits the use of MRI, especially for high resolution or dynamic imaging. Accordingly, many investigators has developed various acceleration techniques to allow fast MR imaging. For the last two decades, one of the most important breakthroughs in this direction is the introduction of compressed sensing (CS) that allows accurate reconstruction from sparsely sampled k-space data. The recent FDA approval of compressed sensing products for clinical scans clearly reflect the maturity of this technology. Therefore, this paper reviews the basic idea of CS and how this technology have been evolved for various MR imaging problems.

Rapid T1 quantification from high resolution 3D data with model-based reconstruction

Purpose

Magnetic resonance imaging protocols for the assessment of quantitative information suffer from long acquisition times since multiple measurements in a parametric dimension are required. To facilitate the clinical applicability, accelerating the acquisition is of high importance. To this end, we propose a model‐based optimization framework in conjunction with undersampling 3D radial stack‐of‐stars data.

Theory and Methods

High resolution 3D T₁ maps are generated from subsampled data by employing model‐based reconstruction combined with a regularization functional, coupling information from the spatial and parametric dimension, to exploit redundancies in the acquired parameter encodings and across parameter maps. To cope with the resulting non‐linear, non‐differentiable optimization problem, we propose a solution strategy based on the iteratively regularized Gauss‐Newton method. The importance of 3D‐spectral regularization is demonstrated by a comparison to 2D‐spectral regularized results. The algorithm is validated for the variable flip angle (VFA) and inversion recovery Look‐Locker (IRLL) method on numerical simulated data, MRI phantoms, and in vivo data.

Results

Evaluation of the proposed method using numerical simulations and phantom scans shows excellent quantitative agreement and image quality. T₁ maps from accelerated 3D in vivo measurements, e.g. 1.8 s/slice with the VFA method, are in high accordance with fully sampled reference reconstructions.

Conclusions

The proposed algorithm is able to recover T₁ maps with an isotropic resolution of 1 mm³ from highly undersampled radial data by exploiting structural similarities in the imaging volume and across parameter maps.

Learning a variational network for reconstruction of accelerated MRI data

PURPOSE

To allow fast and high-quality reconstruction of clinical accelerated multi-coil MR data by learning a variational network that combines the mathematical structure of variational models with deep learning.

THEORY AND METHODS

Generalized compressed sensing reconstruction formulated as a variational model is embedded in an unrolled gradient descent scheme. All parameters of this formulation, including the prior model defined by filter kernels and activation functions as well as the data term weights, are learned during an offline training procedure. The learned model can then be applied online to previously unseen data.

RESULTS

The variational network approach is evaluated on a clinical knee imaging protocol for different acceleration factors and sampling patterns using retrospectively and prospectively undersampled data. The variational network reconstructions outperform standard reconstruction algorithms, verified by quantitative error measures and a clinical reader study for regular sampling and acceleration factor 4.

CONCLUSION

Variational network reconstructions preserve the natural appearance of MR images as well as pathologies that were not included in the training data set. Due to its high computational performance, that is, reconstruction time of 193 ms on a single graphics card, and the omission of parameter tuning once the network is trained, this new approach to image reconstruction can easily be integrated into clinical workflow. Magn Reson Med 79:3055-3071, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Reducing acquisition time for MRI-based forensic age estimation

Radiology-based estimation of a living person’s unknown age has recently attracted increasing attention due to large numbers of undocumented immigrants entering Europe. To avoid the application of X-ray-based imaging techniques, magnetic resonance imaging (MRI) has been suggested as an alternative imaging modality. Unfortunately, MRI requires prolonged acquisition times, which potentially represents an additional stressor for young refugees. To eliminate this shortcoming, we investigated the degree of reduction in acquisition time that still led to reliable age estimates. Two radiologists randomly assessed original images and two sets of retrospectively undersampled data of 15 volunteers (N = 45 data sets) applying an established radiological age estimation method to images of the hand and wrist. Additionally, a neural network-based age estimation method analyzed four sets of further undersampled images from the 15 volunteers (N = 105 data sets). Furthermore, we compared retrospectively undersampled and acquired undersampled data for three volunteers. To assess reliability with increasing degree of undersampling, intra-rater and inter-rater agreement were analyzed computing signed differences and intra-class correlation. While our findings have to be confirmed by a larger prospective study, the results from both radiological and automatic age estimation showed that reliable age estimation was still possible for acquisition times of 15 seconds.

Learning Joint-Sparse Codes for Calibration-Free Parallel MR Imaging

The integration of compressed sensing and parallel imaging (CS-PI) has shown an increased popularity in recent years to accelerate magnetic resonance (MR) imaging. Among them, calibration-free techniques have presented encouraging performances due to its capability in robustly handling the sensitivity information. Unfortunately, existing calibration-free methods have only explored joint-sparsity with direct analysis transform projections. To further exploit joint-sparsity and improve reconstruction accuracy, this paper proposes to Learn joINt-sparse coDes for caliBration-free parallEl mR imaGing (LINDBERG) by modeling the parallel MR imaging problem as an - - minimization objective with an norm constraining data fidelity, Frobenius norm enforcing sparse representation error and the mixed norm triggering joint sparsity across multichannels. A corresponding algorithm has been developed to alternatively update the sparse representation, sensitivity encoded images and K-space data. Then, the final image is produced as the square root of sum of squares of all channel images. Experimental results on both physical phantom and in vivo data sets show that the proposed method is comparable and even superior to state-of-the-art CS-PI reconstruction approaches. Specifically, LINDBERG has presented strong capability in suppressing noise and artifacts while reconstructing MR images from highly undersampled multichannel measurements.

Localizing implanted fiducial markers using undersampled co-RASOR MR imaging

The goal of this work was to use an undersampled, dual-plane centre-out radial sampling acquisition pulse sequence, with off-resonance reception, to localize fiducial markers with reduced acquisition time. Two iterative reconstruction techniques, conjugate gradient CG-SENSE and the variational penalty Total Generalized Variation (TGV), were investigated to minimize the undersampling artifacts in off-resonant radial imaging. Simulations of a field perturber were performed at sub-millimeter resolution and reconstructed to display signal pileups that can be radially compressed towards the geometric centre of the perturber for high contrast visualization, but contrast is non-recoverable as the echo time increases. A cylindrical platinum fiducial marker, placed in a phantom parallel and perpendicular to the B₀-field was imaged with a short-TE half-echo readout. Contrast-to-Noise (CNR) between the signal of the fiducial its adjacent surrounding shell and half-maximum area were used to compare reconstruction methods and undersampling factors. For single slice acquisitions centred about the fiducial, each slice can be performed in as little as 2.8s. The total acquisition time to localize the fiducial marker in a phantom was reduced to 73s by undersampling (R=8) 37 axial and 15 coronal slices, effectively encoding 1.4s/slice. The noise present in undersampled images, for both scan planes and fiducial orientations, decreased significantly using TGV and CG-SENSE reconstructions, with TGV displaying better spatial resolution from reduced half-maximum area.

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.

Partial Discreteness: A Novel Prior for Magnetic Resonance Image Reconstruction

An important factor influencing the quality of magnetic resonance (MR) images is the reconstruction method that is employed, and specifically, the type of prior knowledge that is exploited during reconstruction. In this work, we introduce a new type of prior knowledge, partial discreteness (PD), where a small number of regions in the image are assumed to be homogeneous and can be well represented by a constant magnitude. In particular, we mathematically formalize the partial discreteness property based on a Gaussian Mixture Model (GMM) and derive a partial discreteness image representation that characterizes the salient features of partially discrete images: a constant intensity in homogeneous areas and texture in heterogeneous areas. The partial discreteness representation is then used to construct a novel prior dedicated to the reconstruction of partially discrete MR images. The strength of the proposed prior is demonstrated on various simulated and real k-space data-based experiments with partially discrete images. Results demonstrate that the PD algorithm performs competitively with state-of-the-art reconstruction methods, being flexible and easy to implement.

Reducing slab boundary artifacts in three-dimensional multislab diffusion MRI using nonlinear inversion for slab profile encoding (NPEN)

PURPOSE

To propose a method to reduce the slab boundary artifacts in three-dimensional multislab diffusion MRI.

METHODS

Bloch simulation is used to investigate the effects of multiple factors on slab boundary artifacts, including characterization of residual errors on diffusion quantification. A nonlinear inversion method is proposed to simultaneously estimate the slab profile and the underlying (corrected) image.

RESULTS

Correction results of numerical phantom and in vivo data demonstrate that the method can effectively remove slab boundary artifacts for diffusion data. Notably, the nonlinear inversion is also successful at short TR, a regimen where previously proposed methods (slab profile encoding and weighted average) retain residual artifacts in both diffusion-weighted images and diffusion metrics (mean diffusion coefficient and fractional anisotropy).

CONCLUSION

The nonlinear inversion for removing slab boundary artifacts provides improvements over existing methods, particularly at the short TRs required to maximize SNR efficiency. Magn Reson Med 76:1183-1195, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

ACCELERATING MAGNETIC RESONANCE IMAGING VIA DEEP LEARNING

This paper proposes a deep learning approach for accelerating magnetic resonance imaging (MRI) using a large number of existing high quality MR images as the training datasets. An off-line convolutional neural network is designed and trained to identify the mapping relationship between the MR images obtained from zero-filled and fully-sampled k-space data. The network is not only capable of restoring fine structures and details but is also compatible with online constrained reconstruction methods. Experimental results on real MR data have shown encouraging performance of the proposed method for efficient and effective imaging.

Accelerated Brain DCE-MRI Using Iterative Reconstruction With Total Generalized Variation Penalty for Quantitative Pharmacokinetic Analysis: A Feasibility Study

PURPOSE

To investigate the feasibility of using undersampled k-space data and an iterative image reconstruction method with total generalized variation penalty in the quantitative pharmacokinetic analysis for clinical brain dynamic contrast-enhanced magnetic resonance imaging.

METHODS

Eight brain dynamic contrast-enhanced magnetic resonance imaging scans were retrospectively studied. Two k-space sparse sampling strategies were designed to achieve a simulated image acquisition acceleration factor of 4. They are (1) a golden ratio-optimized 32-ray radial sampling profile and (2) a Cartesian-based random sampling profile with spatiotemporal-regularized sampling density constraints. The undersampled data were reconstructed to yield images using the investigated reconstruction technique. In quantitative pharmacokinetic analysis on a voxel-by-voxel basis, the rate constant K^trans in the extended Tofts model and blood flow F_B and blood volume V_B from the 2-compartment exchange model were analyzed. Finally, the quantitative pharmacokinetic parameters calculated from the undersampled data were compared with the corresponding calculated values from the fully sampled data. To quantify each parameter's accuracy calculated using the undersampled data, error in volume mean, total relative error, and cross-correlation were calculated.

RESULTS

The pharmacokinetic parameter maps generated from the undersampled data appeared comparable to the ones generated from the original full sampling data. Within the region of interest, most derived error in volume mean values in the region of interest was about 5% or lower, and the average error in volume mean of all parameter maps generated through either sampling strategy was about 3.54%. The average total relative error value of all parameter maps in region of interest was about 0.115, and the average cross-correlation of all parameter maps in region of interest was about 0.962. All investigated pharmacokinetic parameters had no significant differences between the result from original data and the reduced sampling data.

CONCLUSION

With sparsely sampled k-space data in simulation of accelerated acquisition by a factor of 4, the investigated dynamic contrast-enhanced magnetic resonance imaging pharmacokinetic parameters can accurately estimate the total generalized variation-based iterative image reconstruction method for reliable clinical application.

Efficient Compressed Sensing SENSE pMRI Reconstruction With Joint Sparsity Promotion

The theory and techniques of compressed sensing (CS) have shown their potential as a breakthrough in accelerating k-space data acquisition for parallel magnetic resonance imaging (pMRI). However, the performance of CS reconstruction models in pMRI has not been fully maximized, and CS recovery guarantees for pMRI are largely absent. To improve reconstruction accuracy from parsimonious amounts of k-space data while maintaining flexibility, a new CS SENSitivity Encoding (SENSE) pMRI reconstruction framework promoting joint sparsity (JS) across channels (JS CS SENSE) is proposed in this paper. The recovery guarantee derived for the proposed JS CS SENSE model is demonstrated to be better than that of the conventional CS SENSE model and similar to that of the coil-by-coil CS model. The flexibility of the new model is better than the coil-by-coil CS model and the same as that of CS SENSE. For fast image reconstruction and fair comparisons, all the introduced CS-based constrained optimization problems are solved with split Bregman, variable splitting, and combined-variable splitting techniques. For the JS CS SENSE model in particular, these techniques lead to an efficient algorithm. Numerical experiments show that the reconstruction accuracy is significantly improved by JS CS SENSE compared with the conventional CS SENSE. In addition, an accurate residual-JS regularized sensitivity estimation model is also proposed and extended to calibration-less (CaL) JS CS SENSE. Numerical results show that CaL JS CS SENSE outperforms other state-of-the-art CS-based calibration-less methods in particular for reconstructing non-piecewise constant images.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

Low-Cost High-Performance MRI

Magnetic Resonance Imaging (MRI) is unparalleled in its ability to visualize anatomical structure and function non-invasively with high spatial and temporal resolution. Yet to overcome the low sensitivity inherent in inductive detection of weakly polarized nuclear spins, the vast majority of clinical MRI scanners employ superconducting magnets producing very high magnetic fields. Commonly found at 1.5-3 tesla (T), these powerful magnets are massive and have very strict infrastructure demands that preclude operation in many environments. MRI scanners are costly to purchase, site, and maintain, with the purchase price approaching $1 M per tesla (T) of magnetic field. We present here a remarkably simple, non-cryogenic approach to high-performance human MRI at ultra-low magnetic field, whereby modern under-sampling strategies are combined with fully-refocused dynamic spin control using steady-state free precession techniques. At 6.5 mT (more than 450 times lower than clinical MRI scanners) we demonstrate (2.5 × 3.5 × 8.5) mm(3) imaging resolution in the living human brain using a simple, open-geometry electromagnet, with 3D image acquisition over the entire brain in 6 minutes. We contend that these practical ultra-low magnetic field implementations of MRI (<10 mT) will complement traditional MRI, providing clinically relevant images and setting new standards for affordable (<$50,000) and robust portable devices.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

A review of 3D first-pass, whole-heart, myocardial perfusion cardiovascular magnetic resonance

A comprehensive review is undertaken of the methods available for 3D whole-heart first-pass perfusion (FPP) and their application to date, with particular focus on possible acceleration techniques. Following a summary of the parameters typically desired of 3D FPP methods, the review explains the mechanisms of key acceleration techniques and their potential use in FPP for attaining 3D acquisitions. The mechanisms include rapid sequences, non-Cartesian k-space trajectories, reduced k-space acquisitions, parallel imaging reconstructions and compressed sensing. An attempt is made to explain, rather than simply state, the varying methods with the hope that it will give an appreciation of the different components making up a 3D FPP protocol. Basic estimates demonstrating the required total acceleration factors in typical 3D FPP cases are included, providing context for the extent that each acceleration method can contribute to the required imaging speed, as well as potential limitations in present 3D FPP literature. Although many 3D FPP methods are too early in development for the type of clinical trials required to show any clear benefit over current 2D FPP methods, the review includes the small but growing quantity of clinical research work already using 3D FPP, alongside the more technical work. Broader challenges concerning FPP such as quantitative analysis are not covered, but challenges with particular impact on 3D FPP methods, particularly with regards to motion effects, are discussed along with anticipated future work in the field.

P-LORAKS: Low-rank modeling of local k-space neighborhoods with parallel imaging data

PURPOSE

To propose and evaluate P-LORAKS a new calibrationless parallel imaging reconstruction framework.

THEORY AND METHODS

LORAKS is a flexible and powerful framework that was recently proposed for constrained MRI reconstruction. LORAKS was based on the observation that certain matrices constructed from fully sampled k-space data should have low rank whenever the image has limited support or smooth phase, and made it possible to accurately reconstruct images from undersampled or noisy data using low-rank regularization. This paper introduces P-LORAKS, which extends LORAKS to the context of parallel imaging. This is achieved by combining the LORAKS matrices from different channels to yield a larger but more parsimonious low-rank matrix model of parallel imaging data. This new model can be used to regularize the reconstruction of undersampled parallel imaging data, and implicitly imposes phase, support, and parallel imaging constraints without needing to calibrate phase, support, or sensitivity profiles.

RESULTS

The capabilities of P-LORAKS are evaluated with retrospectively undersampled data and compared against existing parallel MRI reconstruction methods. Results show that P-LORAKS can improve parallel imaging reconstruction quality, and can enable the use of new k-space trajectories that are not compatible with existing reconstruction methods.

CONCLUSION

The P-LORAKS framewok provides a new and effective way to regularize parallel imaging reconstruction.

An efficient calculation method for pharmacokinetic parameters in brain permeability study using dynamic contrast-enhanced MRI

PURPOSE

To develop an efficient method for calculating pharmacokinetic (PK) parameters in brain DCE-MRI permeability studies.

METHODS

A linear least-squares fitting algorithm based on a derivative expression of the two-compartment PK model was proposed to analytically solve for the PK parameters. Noise in the expression was minimized through low-pass filtering. Simulation studies were conducted in which the proposed method was compared with two existing methods in terms of accuracy and efficiency. Five in vivo brain studies were demonstrated for potential clinical application.

RESULTS

In the simulation studies using chosen parameter values, the calculated percent difference of K(trans) by the proposed method was <5.0% with a temporal resolution (Δt) < 5 s, and the accuracies of all parameter results were better or comparable to existing methods. When analyzed within certain parameter intensity ranges, the proposed method was more accurate than the existing methods and improved the efficiency by a factor of up to 458 for a Δt = 1 s and up to 38 for a Δt = 5 s. In the in vivo study, the calculated parameters using the proposed method were comparable to those using the existing methods with improved efficiencies.

CONCLUSIONS

An efficient method was developed for the accurate and efficient calculation of parameters in brain DCE-MRI permeability studies.

A model-based reconstruction for undersampled radial spin-echo DTI with variational penalties on the diffusion tensor

Radial spin-echo diffusion imaging allows motion-robust imaging of tissues with very low T2 values like articular cartilage with high spatial resolution and signal-to-noise ratio (SNR). However, in vivo measurements are challenging, due to the significantly slower data acquisition speed of spin-echo sequences and the less efficient k-space coverage of radial sampling, which raises the demand for accelerated protocols by means of undersampling. This work introduces a new reconstruction approach for undersampled diffusion-tensor imaging (DTI). A model-based reconstruction implicitly exploits redundancies in the diffusion-weighted images by reducing the number of unknowns in the optimization problem and compressed sensing is performed directly in the target quantitative domain by imposing a total variation (TV) constraint on the elements of the diffusion tensor. Experiments were performed for an anisotropic phantom and the knee and brain of healthy volunteers (three and two volunteers, respectively). Evaluation of the new approach was conducted by comparing the results with reconstructions performed with gridding, combined parallel imaging and compressed sensing and a recently proposed model-based approach. The experiments demonstrated improvements in terms of reduction of noise and streaking artifacts in the quantitative parameter maps, as well as a reduction of angular dispersion of the primary eigenvector when using the proposed method, without introducing systematic errors into the maps. This may enable an essential reduction of the acquisition time in radial spin-echo diffusion-tensor imaging without degrading parameter quantification and/or SNR.

Fast quantitative susceptibility mapping using 3D EPI and total generalized variation

Quantitative susceptibility mapping (QSM) allows new insights into tissue composition and organization by assessing its magnetic property. Previous QSM studies have already demonstrated that magnetic susceptibility is highly sensitive to myelin density and fiber orientation as well as to para- and diamagnetic trace elements. Image resolution in QSM with current approaches is limited by the long acquisition time of 3D scans and the need for high signal to noise ratio (SNR) to solve the dipole inversion problem. We here propose a new total-generalized-variation (TGV) based method for QSM reconstruction, which incorporates individual steps of phase unwrapping, background field removal and dipole inversion in a single iteration, thus yielding a robust solution to the reconstruction problem. This approach has beneficial characteristics for low SNR data, allowing for phase data to be rapidly acquired with a 3D echo planar imaging (EPI) sequence. The proposed method was evaluated with a numerical phantom and in vivo at 3 and 7 T. Compared to total variation (TV), TGV-QSM enforced higher order smoothness which yielded solutions closer to the ground truth and prevented stair-casing artifacts. The acquisition time for images with 1mm isotropic resolution and whole brain coverage was 10s on a clinical 3 Tesla scanner. In conclusion, 3D EPI acquisition combined with single-step TGV reconstruction yields reliable QSM images of the entire brain with 1mm isotropic resolution in seconds. The short acquisition time combined with the robust reconstruction may enable new QSM applications in less compliant populations, clinical susceptibility tensor imaging, and functional resting state examinations.

Free-breathing, zero-TE MR lung imaging

OBJECT

The investigation of three-dimensional radial, zero-echo time (TE) imaging for high-resolution, free-breathing magnetic resonance (MR) lung imaging using prospective and retrospective motion correction.

MATERIALS AND METHODS

Zero-TE was implemented similarly to the rotating-ultra-fast-imaging-sequence, providing 3D, isotropic, radial imaging with proton density contrast. Respiratory motion was addressed using prospective triggering (PT), prospective gating (PG) and retrospective gating (RG) with physiological signals obtained from a respiratory belt and interleaved pencil beam and DC navigators. The methods were demonstrated on four healthy volunteers at 3T.

RESULTS

3D, radial zero-TE imaging with high imaging bandwidth and nominally zero echo-time enables efficient capture of short-lived signals from the lung parenchyma and the vessels. Compared to Cartesian encoding, unaccounted for free-breathing respiration resulted in only benign blurring artifacts confined to the origin of motion. Breath holding froze respiration but achieved only limited image resolution (~1.8 mm, 30 s). PT and PG obtained similar quality expiratory-phase images at 1.2 mm resolution in ~6 min scan time. RG allowed multi-phase imaging in ~15 min, derived from eight individually stored averages.

CONCLUSION

Zero-TE appears to be an attractive pulse sequence for 3D isotropic lung imaging. Prospective and retrospective approaches provide high-quality, free-breathing MR lung imaging within reasonable scan time.

Acceleration and motion-correction techniques for high-resolution intravascular MRI

PURPOSE

High-resolution intravascular (IV) MRI is susceptible to degradation from physiological motion and requires high frame-rates for true endoscopy. Traditional cardiac-gating techniques compromise efficiency by reducing the effective scan rate. Here we test whether compressed sensing (CS) reconstruction and ungated motion-compensation using projection shifting, could provide faster motion-suppressed, IVMRI.

THEORY AND METHODS

CS reconstruction is developed for undersampled Cartesian and radial imaging using a new IVMRI-specific cost function to effectively increase imaging speed. A new motion correction method is presented wherein individual IVMRI projections are shifted based on the IVMRI detector's intrinsic amplitude and phase properties. The methods are tested at 3 Tesla (T) in fruit, human vessel specimens, and a rabbit aorta in vivo. Images are compared using structural-similarity and "spokal variation" indices.

RESULTS

Although some residual artifacts persisted, CS acceleration and radial motion compensation strategies reduced motion artifact in vitro and in vivo, allowing effective accelerations of up to eight-fold at 200-300 µm resolution.

CONCLUSION

The 3T IVMRI detectors are well-suited to CS and motion correction strategies based on their intrinsic radially-sparse sensitivity profiles and high signal-to-noise ratios.

Aggregated motion estimation for real-time MRI reconstruction

PURPOSE

In real-time MRI serial images are generally reconstructed from highly undersampled datasets as the iterative solutions of an inverse problem. While practical realizations based on regularized nonlinear inversion (NLINV) have hitherto been surprisingly successful, strong assumptions about the continuity of image features may affect the temporal fidelity of the estimated reconstructions.

THEORY AND METHODS

The proposed method for real-time image reconstruction integrates the deformations between nearby frames into the data consistency term of the inverse problem. The aggregated motion estimation (AME) is not required to be affine or rigid and does not need additional measurements. Moreover, it handles multi-channel MRI data by simultaneously determining the image and its coil sensitivity profiles in a nonlinear formulation which also adapts to non-Cartesian (e.g., radial) sampling schemes. The new method was evaluated for real-time MRI studies using highly undersampled radial gradient-echo sequences.

RESULTS

AME reconstructions for a motion phantom with controlled speed as well as for measurements of human heart and tongue movements demonstrate improved temporal fidelity and reduced residual undersampling artifacts when compared with NLINV reconstructions without motion estimation.

CONCLUSION

Nonlinear inverse reconstructions with aggregated motion estimation offer improved image quality and temporal acuity for visualizing rapid dynamic processes by real-time MRI.

Highly accelerated projection imaging with coil sensitivity encoding for rapid MRI

PURPOSE

Rapid magnetic resonance imaging (MRI) acquisition is typically achieved by acquiring all or most lines of k-space after one radio frequency (RF) excitation. Parallel imaging techniques can further accelerate data acquisition by acquiring fewer phase-encoded lines and utilizing the spatial sensitivity information of the RF coil arrays. The goal of this study was to develop a new MRI data acquisition and reconstruction technique that is capable of reconstructing a two-dimensional (2D) image using highly undersampled k-space data without any special hardware. Such a technique would be very efficient, as it would significantly reduce the time wasted during multiple RF excitations or phase encoding and gradient switching periods.

METHODS

The essence of this new technique is to densely sample a small number of projections, which should be acquired at an angle other than 0° or multiples of 45°. This results in multiple rays passing through a voxel and provides new and independent measurements for each voxel. Then the images are reconstructed using the unique information coming from these projections combined with RF coil sensitivity profiles. The feasibility of this new technique was investigated with realistic simulations and experimental studies using a phantom and compared with conventional nonuniform fast Fourier transform technique. Eigenvalue analysis and error calculations were conducted to find optimal projection angles and minimum requirements for dense sampling.

RESULTS

Reconstruction of 64 × 64 images was done using a single projection from simulated data under different noise levels. Simulated reconstruction was also tested with two projections to assess the improvement. Experimental phantom images were reconstructed at higher resolution using 4, 8, and 16 projections. Cross-sectional profiles illustrate that the new technique resolved compartment boundaries clearly.

CONCLUSIONS

Simulations demonstrated that only a single k-space line might be sufficient to reconstruct a 2D image using this new technique. Experimental results showed that this is a promising new technique for fast imaging. Using the information from the simulations and fast imaging parameters published in the literature, it could be predicted that a two-dimensional image could be acquired in about 10 ms. One of the major advantages of this new technique is that it does not require any additional hardware and can be implemented on a conventional scanner with an eight-channel coil.

Compressed sensing reconstruction for whole-heart imaging with 3D radial trajectories: a graphics processing unit implementation

A disadvantage of three-dimensional (3D) isotropic acquisition in whole-heart coronary MRI is the prolonged data acquisition time. Isotropic 3D radial trajectories allow undersampling of k-space data in all three spatial dimensions, enabling accelerated acquisition of the volumetric data. Compressed sensing (CS) reconstruction can provide further acceleration in the acquisition by removing the incoherent artifacts due to undersampling and improving the image quality. However, the heavy computational overhead of the CS reconstruction has been a limiting factor for its application. In this article, a parallelized implementation of an iterative CS reconstruction method for 3D radial acquisitions using a commercial graphics processing unit is presented. The execution time of the graphics processing unit-implemented CS reconstruction was compared with that of the C++ implementation, and the efficacy of the undersampled 3D radial acquisition with CS reconstruction was investigated in both phantom and whole-heart coronary data sets. Subsequently, the efficacy of CS in suppressing streaking artifacts in 3D whole-heart coronary MRI with 3D radial imaging and its convergence properties were studied. The CS reconstruction provides improved image quality (in terms of vessel sharpness and suppression of noise-like artifacts) compared with the conventional 3D gridding algorithm, and the graphics processing unit implementation greatly reduces the execution time of CS reconstruction yielding 34-54 times speed-up compared with C++ implementation.