Reference-free single-pass EPI Nyquist ghost correction using annihilating filter-based low rank Hankel matrix (ALOHA)

Dynamic field mapping and distortion correction using single-shot blip-rewound EPI and joint multi-echo reconstruction

PURPOSE

To develop a method for dynamic∆ B 0 $$ \Delta {B}_0 $$ mapping and distortion correction.

METHODS

A blip-rewound EPI trajectory was developed to acquire multiple 2D EPI images in a single readout with an interleaved order, which allows a short TE difference. A joint multi-echo reconstruction was utilized to exploit the shared information between EPI images. The reconstructed images from each readout are combined to produce a final magnitude image. A∆ B 0 $$ \Delta {B}_0 $$ map is calculated from the phase of these images for distortion correction. The efficacy of the proposed method is assessed with phantom and in vivo experiments. The performance of the proposed method in the presence of subject motion is also investigated.

RESULTS

Compared to conventional multi-echo EPI, the proposed method allows dynamic∆ B 0 $$ \Delta {B}_0 $$ mapping at matched resolution with a much shorter TR. Phantom and in vivo results show that the proposed method can provide a comparable magnitude image as conventional single-shot EPI. The∆ B 0 $$ \Delta {B}_0 $$ maps calculated from the proposed method are consistent with conventional multi-echo EPI in the phantom experiment. For in vivo experiments, the proposed method provides a more accurate estimation of∆ B 0 $$ \Delta {B}_0 $$ than conventional multi-echo EPI, which is prone to phase wrapping problems due to the long TE difference. In-vivo scan with subject motion shows the proposed dynamic field mapping method can improve the temporal stability of EPI time series compared to gradient echo (GRE) based static field mapping.

CONCLUSION

The proposed method allows accurate dynamic∆ B 0 $$ \Delta {B}_0 $$ mapping for robust distortion correction without compromising spatial or temporal resolution.

Model-based iterative reconstruction for direct imaging with point spread function encoded echo planar MRI

BACKGROUND

Echo planar imaging (EPI) is a fast measurement technique commonly used in magnetic resonance imaging (MRI), but is highly sensitive to measurement non-idealities in reconstruction. Point spread function (PSF)-encoded EPI is a multi-shot strategy which alleviates distortion, but acquisition of encodings suitable for direct distortion-free imaging prolongs scan time. In this work, a model-based iterative reconstruction (MBIR) framework is introduced for direct imaging with PSF-EPI to improve image quality and acceleration potential.

METHODS

An MBIR platform was developed for accelerated PSF-EPI. The reconstruction utilizes a subspace representation, is regularized to promote local low-rankedness (LLR), and uses variable splitting for efficient iteration. Comparisons were made against standard reconstructions from prospectively accelerated PSF-EPI data and with retrospective subsampling. Exploring aggressive partial Fourier acceleration of the PSF-encoding dimension, additional comparisons were made against an extension of Homodyne to direct PSF-EPI in numerical experiments. A neuroradiologists' assessment was completed comparing images reconstructed with MBIR from retrospectively truncated data directly against images obtained with standard reconstructions from non-truncated datasets.

RESULTS

Image quality results were consistently superior for MBIR relative to standard and Homodyne reconstructions. As the MBIR signal model and reconstruction allow for arbitrary sampling of the PSF space, random sampling of the PSF-encoding dimension was also demonstrated, with quantitative assessments indicating best performance achieved through nonuniform PSF sampling combined with partial Fourier. With retrospective subsampling, MBIR reconstructs high-quality images from sub-minute scan datasets. MBIR was shown to be superior in a neuroradiologists' assessment with respect to three of five performance criteria, with equivalence for the remaining two.

CONCLUSIONS

A novel image reconstruction framework is introduced for direct imaging with PSF-EPI, enabling arbitrary PSF space sampling and reconstruction of diagnostic-quality images from highly accelerated PSF-encoded EPI data.

Referenceless Nyquist ghost correction outperforms standard navigator-based method and improves efficiency of in vivo diffusion tensor cardiovascular magnetic resonance

PURPOSE

The study aims to assess the potential of referenceless methods of EPI ghost correction to accelerate the acquisition of in vivo diffusion tensor cardiovascular magnetic resonance (DT-CMR) data using both computational simulations and data from in vivo experiments.

METHODS

Three referenceless EPI ghost correction methods were evaluated on mid-ventricular short axis DT-CMR spin echo and STEAM datasets from 20 healthy subjects at 3T. The reduced field of view excitation technique was used to automatically quantify the Nyquist ghosts, and DT-CMR images were fit to a linear ghost model for correction.

RESULTS

Numerical simulation showed the singular value decomposition (SVD) method is the least sensitive to noise, followed by Ghost/Object method and entropy-based method. In vivo experiments showed significant ghost reduction for all correction methods, with referenceless methods outperforming navigator methods for both spin echo and STEAM sequences at b = 32, 150, 450, and 600  smm - 2 $$ {\mathrm{smm}}^{-2} $$ . It is worth noting that as the strength of the diffusion encoding increases, the performance gap between the referenceless method and the navigator-based method diminishes.

CONCLUSION

Referenceless ghost correction effectively reduces Nyquist ghost in DT-CMR data, showing promise for enhancing the accuracy and efficiency of measurements in clinical practice without the need for any additional reference scans.

Reconstruction for 7T high-resolution whole-brain diffusion MRI using two-stage N/2 ghost correction and L1-SPIRiT without single-band reference

PURPOSE

To combine a new two-stage N/2 ghost correction and an adapted L1-SPIRiT method for reconstruction of 7T highly accelerated whole-brain diffusion MRI (dMRI) using only autocalibration scans (ACS) without the need of additional single-band reference (SBref) scans.

METHODS

The proposed ghost correction consisted of a 3-line reference approach in stage 1 and the reference-free entropy method in stage 2. The adapted L1-SPIRiT method was formulated within the 3D k-space framework. Its efficacy was examined by acquiring two dMRI data sets at 1.05-mm isotropic resolutions with a total acceleration of 6 or 9 (i.e., 2-fold or 3-fold slice and 3-fold in-plane acceleration). Diffusion analysis was performed to derive DTI metrics and estimate fiber orientation distribution functions (fODFs). The results were compared with those of 3D k-space GRAPPA using only ACS, all in reference to 3D k-space GRAPPA using both ACS and SBref (serving as a reference).

RESULTS

The proposed ghost correction eliminated artifacts more robustly than conventional approaches. Our adapted L1-SPIRiT method outperformed 3D k-space GRAPPA when using only ACS, improving image quality to what was achievable with 3D k-space GRAPPA using both ACS and SBref scans. The improvement in image quality further resulted in an improvement in estimation performances for DTI and fODFs.

CONCLUSION

The combination of our new ghost correction and adapted L1-SPIRiT method can reliably reconstruct 7T highly accelerated whole-brain dMRI without the need of SBref scans, increasing acquisition efficiency and reducing motion sensitivity.

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.

Improving robustness of 3D multi-shot EPI by structured low-rank reconstruction of segmented CAIPI sampling for fMRI at 7T

Three-dimensional (3D) encoding methods are increasingly being explored as alternatives to two-dimensional (2D) multi-slice acquisitions in fMRI, particularly in cases where high isotropic resolution is needed. 3D multi-shot EPI acquisition, as the workhorse of 3D fMRI imaging, is susceptible to physiological fluctuations which can induce inter-shot phase variations, and thus reducing the achievable tSNR, negating some of the benefit of 3D encoding. This issue can be particularly problematic at ultra-high fields like 7T, which have more severe off-resonance effects. In this work, we aim to improve the temporal stability of 3D multi-shot EPI at 7T by improving its robustness to inter-shot phase variations. We presented a 3D segmented CAIPI sampling trajectory ("seg-CAIPI") and an improved reconstruction method based on Hankel structured low-rank matrix recovery. Simulation and in-vivo results demonstrate that the combination of the seg-CAIPI sampling scheme and the proposed structured low-rank reconstruction is a promising way to effectively reduce the unwanted temporal variance induced by inter-shot physiological fluctuations, and thus improve the robustness of 3D multi-shot EPI for fMRI.

High-fidelity, high-spatial-resolution diffusion magnetic resonance imaging of ex vivo whole human brain at ultra-high gradient strength with structured low-rank echo-planar imaging ghost correction

Diffusion magnetic resonance imaging (dMRI) of whole ex vivo human brain specimens enables three-dimensional (3D) mapping of structural connectivity at the mesoscopic scale, providing detailed evaluation of fiber architecture and tissue microstructure at a spatial resolution that is difficult to access in vivo. To account for the short T2 and low diffusivity of fixed tissue, ex vivo dMRI is often acquired using strong diffusion-sensitizing gradients and multishot/segmented 3D echo-planar imaging (EPI) sequences to achieve high spatial resolution. However, the combination of strong diffusion-sensitizing gradients and multishot/segmented EPI readout can result in pronounced ghosting artifacts incurred by nonlinear spatiotemporal variations in the magnetic field produced by eddy currents. Such ghosting artifacts cannot be corrected with conventional correction solutions and pose a significant roadblock to leveraging human MRI scanners with ultrahigh gradients for ex vivo whole-brain dMRI. Here, we show that ghosting-correction approaches that correct for either polarity-related ghosting or shot-to-shot variations in a separate manner are suboptimal for 3D multishot diffusion-weighted EPI experiments in fixed human brain specimens using strong diffusion-sensitizing gradients on the 3-T Connectom MRI scanner, resulting in orientationally biased dMRI estimates. We apply a recently developed advanced k-space reconstruction method based on structured low-rank matrix (SLM) modeling that handles both polarity-related ghosting and shot-to-shot variation simultaneously, to mitigate artifacts in high-angular resolution multishot dMRI data acquired in several fixed human brain specimens at 0.7-0.8-mm isotropic spatial resolution using b-values up to 10,000 s/mm2 and gradient strengths up to 280 mT/m. We demonstrate the improved mapping of diffusion tensor imaging and fiber orientation distribution functions in key neuroanatomical areas distributed across the whole brain using SLM-based EPI ghost correction compared with alternative techniques.

Multi-band multi-shot diffusion MRI reconstruction with joint usage of structured low-rank constraints and explicit phase mapping

PURPOSE

To develop a joint reconstruction method for multi-band multi-shot diffusion MRI.

THEORY AND METHODS

Multi-band multi-shot EPI acquisition is an effective approach for high-resolution diffusion MRI, but requires specific algorithms to correct the inter-shot phase variations. The phase correction can be done by first estimating the explicit phase map and then feeding it into the k-space signal formulation model. Alternatively, the phase information can be used indirectly as structured low-rank constraints in k-space. The 2 methods differ in reconstruction accuracy and efficiency. We aim to combine the 2 different approaches for improved image quality and reconstruction efficiency simultaneously, termed "joint usage of structured low-rank constraints and explicit phase mapping" (JULEP). The proposed JULEP reconstruction is tested on both single-band and multi-band, multi-shot diffusion data, with different resolutions and b values. The results of JULEP are compared with conventional methods with explicit phase mapping (i.e., multiplexed sensitivity-encoding [MUSE]) and structured low-rank constraints (i.e., MUSSELS), and another joint reconstruction method (i.e., network estimated artifacts for tempered reconstruction [NEATR]).

RESULTS

JULEP improves the quality of the navigator and subsequently facilitates the reconstruction of final diffusion images. Compared with all 3 other methods (MUSE, MUSSELS, and NEATR), JULEP mitigates residual structural bias and improves temporal SNRs in the final diffusion image, particularly at high multi-band factors. Compared with MUSSELS, JULEP also improves computational efficiency.

CONCLUSION

The proposed JULEP method significantly improves the image quality and reconstruction efficiency of multi-band multi-shot diffusion MRI, which can promote a broader application of high-resolution diffusion MRI.

Low rank off-resonance correction for double half-echo k-space acquisitions

The present study describes a model-based approach for correcting off-resonance in the context of double half-echo k-space acquisitions. This technique employs center-out readouts in forward and reverse directions to reduce echo-times but is sensitive to off-resonance, which manifests as pixel shifts in both directions. Demodulating the k-space signal with a constant off-resonance term per slice removes pixel shifts and results in a marked reduction in blurring. Phantom and in vivo datasets are demonstrated from low bandwidth sodium imaging.

Highly accelerated EPI with wave encoding and multi-shot simultaneous multislice imaging

PURPOSE

To introduce wave-encoded acquisition and reconstruction techniques for highly accelerated EPI with reduced g-factor penalty and image artifacts.

THEORY AND METHODS

Wave-EPI involves application of sinusoidal gradients during the EPI readout, which spreads the aliasing in all spatial directions, thereby taking better advantage of 3D coil sensitivity profiles. The amount of voxel spreading that can be achieved by the wave gradients during the short EPI readout period is constrained by the slew rate of the gradient coils and peripheral nerve stimulation monitor. We propose to use a "half-cycle" sinusoidal gradient to increase the amount of voxel spreading that can be achieved while respecting the slew and stimulation constraints. Extending wave-EPI to multi-shot acquisition minimizes geometric distortion and voxel blurring at high in-plane resolutions, while structured low-rank regularization mitigates shot-to-shot phase variations. To address gradient imperfections, we propose to use different point spread functions for the k-space lines with positive and negative polarities, which are calibrated with a FLEET-based reference scan.

RESULTS

Wave-EPI enabled whole-brain single-shot gradient-echo (GE) and multi-shot spin-echo (SE) EPI acquisitions at high acceleration factors at 3T and was combined with g-Slider encoding to boost the SNR level in 1 mm isotropic diffusion imaging. Relative to blipped-CAIPI, wave-EPI reduced average and maximum g-factors by up to 1.21- and 1.37-fold at R_in  × R_sms  = 3 × 3, respectively.

CONCLUSION

Wave-EPI allows highly accelerated single- and multi-shot EPI with reduced g-factor and artifacts and may facilitate clinical and neuroscientific applications of EPI by improving the spatial and temporal resolution in functional and diffusion imaging.

Calibrationless multi-slice Cartesian MRI via orthogonally alternating phase encoding direction and joint low-rank tensor completion

We propose a multi-slice acquisition with orthogonally alternating phase encoding (PE) direction and subsequent joint calibrationless reconstruction for accelerated multiple individual 2D slices or multi-slice 2D Cartesian MRI. Specifically, multi-slice multi-channel data are first acquired with random or uniform PE undersampling while orthogonally alternating PE direction between adjacent slices. They are then jointly reconstructed through a recently developed low-rank multi-slice Hankel tensor completion (MS-HTC) approach. The proposed acquisition and reconstruction strategy was evaluated with human brain MR data. It effectively suppressed aliasing artifacts even at high acceleration factor, outperforming the existing MS-HTC approach, where PE direction is the same between adjacent slices. More importantly, the new strategy worked robustly with uniform undersampling or random undersampling without any consecutive central k-space lines. In summary, our proposed multi-slice MRI strategy exploits both coil sensitivity and image content similarities across adjacent slices. Orthogonally alternating PE direction among slices substantially facilitates the low-rank completion process and improves image reconstruction quality. This new strategy is applicable to uniform and random PE undersampling. It can be easily implemented in practice for Cartesian parallel imaging of multiple individual 2D slices without any coil sensitivity calibration.

EPI phase error correction with deep learning (PEC-DL) at 7 T

PURPOSE

The phase mismatch between odd and even echoes in EPI causes Nyquist ghost artifacts. Existing ghost correction methods often suffer from severe residual artifacts and are ineffective with k-space undersampling data. This study proposed a deep learning-based method (PEC-DL) to correct phase errors for DWI at 7 Tesla.

METHODS

The acquired k-space data were divided into 2 independent undersampled datasets according to their readout polarities. Then the proposed PEC-DL network reconstructed 2 ghost-free images using the undersampled data without calibration and navigator data. The network was trained with fully sampled images and applied to two- and fourfold accelerated data. Healthy volunteers and patients with Moyamoya disease were recruited to validate the efficacy of the PEC-DL method.

RESULTS

The PEC-DL method was capable to mitigate the ghost artifacts in DWI in healthy volunteers as well as patients with Moyamoya disease. The fourfold accelerated results showed much less distortion in the lesions of the Moyamoya patient using high b-value DWI and the corresponding ADC maps. The ghost-to-signal ratios were significantly lower in PEC-DL images compared to conventional linear phase corrections, mini-entropy, and PEC-GRAPPA algorithms.

CONCLUSION

The proposed method can effectively eliminate ghost artifacts for full sampled and up to fourfold accelerated EPI data without calibration and navigator data.

End-to-end deep learning for interior tomography with low-dose x-ray CT

Objective. There are several x-ray computed tomography (CT) scanning strategies used to reduce radiation dose, such as (1) sparse-view CT, (2) low-dose CT and (3) region-of-interest (ROI) CT (called interior tomography). To further reduce the dose, sparse-view and/or low-dose CT settings can be applied together with interior tomography. Interior tomography has various advantages in terms of reducing the number of detectors and decreasing the x-ray radiation dose. However, a large patient or a small field-of-view (FOV) detector can cause truncated projections, and then the reconstructed images suffer from severe cupping artifacts. In addition, although low-dose CT can reduce the radiation exposure dose, analytic reconstruction algorithms produce image noise. Recently, many researchers have utilized image-domain deep learning (DL) approaches to remove each artifact and demonstrated impressive performances, and the theory of deep convolutional framelets supports the reason for the performance improvement. Approach. In this paper, we found that it is difficult to solve coupled artifacts using an image-domain convolutional neural network (CNN) based on deep convolutional framelets. Significance. To address the coupled problem, we decouple it into two sub-problems: (i) image-domain noise reduction inside the truncated projection to solve low-dose CT problem and (ii) extrapolation of the projection outside the truncated projection to solve the ROI CT problem. The decoupled sub-problems are solved directly with a novel proposed end-to-end learning method using dual-domain CNNs. Main results. We demonstrate that the proposed method outperforms the conventional image-domain DL methods, and a projection-domain CNN shows better performance than the image-domain CNNs commonly used by many researchers.

What's new and what's next in diffusion MRI preprocessing

Diffusion MRI (dMRI) provides invaluable information for the study of tissue microstructure and brain connectivity, but suffers from a range of imaging artifacts that greatly challenge the analysis of results and their interpretability if not appropriately accounted for. This review will cover dMRI artifacts and preprocessing steps, some of which have not typically been considered in existing pipelines or reviews, or have only gained attention in recent years: brain/skull extraction, B-matrix incompatibilities w.r.t the imaging data, signal drift, Gibbs ringing, noise distribution bias, denoising, between- and within-volumes motion, eddy currents, outliers, susceptibility distortions, EPI Nyquist ghosts, gradient deviations, B1 bias fields, and spatial normalization. The focus will be on "what's new" since the notable advances prior to and brought by the Human Connectome Project (HCP), as presented in the predecessing issue on "Mapping the Connectome" in 2013. In addition to the development of novel strategies for dMRI preprocessing, exciting progress has been made in the availability of open source tools and reproducible pipelines, databases and simulation tools for the evaluation of preprocessing steps, and automated quality control frameworks, amongst others. Finally, this review will consider practical considerations and our view on "what's next" in dMRI preprocessing.

Minimizing echo and repetition times in magnetic resonance imaging using a double half-echo k-space acquisition and low-rank reconstruction

Sampling k-space asymmetrically (ie, partial Fourier sampling) in the readout direction is a common way to reduce the echo time (TE) during magnetic resonance image acquisitions. This technique requires overlap around the center of k-space to provide a calibration region for reconstruction, which limits the minimum fractional echo to ~60% before artifacts are observed. The present study describes a method for reconstructing images from exact half echoes using two separate acquisitions with reversed readout polarity, effectively providing a full line of k-space without additional data around central k-space. This approach can benefit sequences or applications that prioritize short TE, short inter-echo spacing or short repetition time. An example of the latter is demonstrated to reduce banding artifacts in balanced steady-state free precession.

Unpaired Training of Deep Learning tMRA for Flexible Spatio-Temporal Resolution

Time-resolved MR angiography (tMRA) has been widely used for dynamic contrast enhanced MRI (DCE-MRI) due to its highly accelerated acquisition. In tMRA, the periphery of the k -space data are sparsely sampled so that neighbouring frames can be merged to construct one temporal frame. However, this view-sharing scheme fundamentally limits the temporal resolution, and it is not possible to change the view-sharing number to achieve different spatio-temporal resolution trade-offs. Although many deep learning approaches have been recently proposed for MR reconstruction from sparse samples, the existing approaches usually require matched fully sampled k -space reference data for supervised training, which is not suitable for tMRA due to the lack of high spatio-temporal resolution ground-truth images. To address this problem, here we propose a novel unpaired training scheme for deep learning using optimal transport driven cycle-consistent generative adversarial network (cycleGAN). In contrast to the conventional cycleGAN with two pairs of generator and discriminator, the new architecture requires just a single pair of generator and discriminator, which makes the training much simpler but still improves the performance. Reconstruction results using in vivo tMRA and simulation data set confirm that the proposed method can immediately generate high quality reconstruction results at various choices of view-sharing numbers, allowing us to exploit better trade-off between spatial and temporal resolution in time-resolved MR angiography.

Robust autocalibrated structured low-rank EPI ghost correction

PURPOSE

We propose and evaluate a new structured low-rank method for echo-planar imaging (EPI) ghost correction called Robust Autocalibrated LORAKS (RAC-LORAKS). The method can be used to suppress EPI ghosts arising from the differences between different readout gradient polarities and/or the differences between different shots. It does not require conventional EPI navigator signals, and is robust to imperfect autocalibration data.

METHODS

Autocalibrated LORAKS is a previous structured low-rank method for EPI ghost correction that uses GRAPPA-type autocalibration data to enable high-quality ghost correction. This method works well when the autocalibration data are pristine, but performance degrades substantially when the autocalibration information is imperfect. RAC-LORAKS generalizes Autocalibrated LORAKS in two ways. First, it does not completely trust the information from autocalibration data, and instead considers the autocalibration and EPI data simultaneously when estimating low-rank matrix structure. Second, it uses complementary information from the autocalibration data to improve EPI reconstruction in a multi-contrast joint reconstruction framework. RAC-LORAKS is evaluated using simulations and in vivo data, including comparisons to state-of-the-art methods.

RESULTS

RAC-LORAKS is demonstrated to have good ghost elimination performance compared to state-of-the-art methods in several complicated EPI acquisition scenarios (including gradient-echo brain imaging, diffusion-encoded brain imaging, and cardiac imaging).

CONCLUSIONS

RAC-LORAKS provides effective suppression of EPI ghosts and is robust to imperfect autocalibration data.

Parallel imaging with a combination of sensitivity encoding and generative adversarial networks

Background

Magnetic resonance imaging (MRI) has the limitation of low imaging speed. Acceleration methods using under-sampled k-space data have been widely exploited to improve data acquisition without reducing the image quality. Sensitivity encoding (SENSE) is the most commonly used method for multi-channel imaging. However, SENSE has the drawback of severe g-factor artifacts when the under-sampling factor is high. This paper applies generative adversarial networks (GAN) to remove g-factor artifacts from SENSE reconstructions.

Methods

Our method was evaluated on a public knee database containing 20 healthy participants. We compared our method with conventional GAN using zero-filled (ZF) images as input. Structural similarity (SSIM), peak signal to noise ratio (PSNR), and normalized mean square error (NMSE) were calculated for the assessment of image quality. A paired student's t-test was conducted to compare the image quality metrics between the different methods. Statistical significance was considered at P<0.01.

Results

The proposed method outperformed SENSE, variational network (VN), and ZF + GAN methods in terms of SSIM (SENSE + GAN: 0.81±0.06, SENSE: 0.40±0.07, VN: 0.79±0.06, ZF + GAN: 0.77±0.06), PSNR (SENSE + GAN: 31.90±1.66, SENSE: 22.70±1.99, VN: 31.35±2.01, ZF + GAN: 29.95±1.59), and NMSE (×10^-7) (SENSE + GAN: 0.95±0.34, SENSE: 4.81±1.33, VN: 0.97±0.30, ZF + GAN: 1.60±0.84) with an under-sampling factor of up to 6-fold.

Conclusions

This study demonstrated the feasibility of using GAN to improve the performance of SENSE reconstruction. The improvement of reconstruction is more obvious for higher under-sampling rates, which shows great potential for many clinical applications.

Calibrationless parallel imaging reconstruction for multislice MR data using low-rank tensor completion

PURPOSE

To provide joint calibrationless parallel imaging reconstruction of highly accelerated multislice 2D MR k-space data.

METHODS

Adjacent image slices in multislice MR data have similar coil sensitivity maps, spatial support, and image content. Such similarities can be utilized to improve image quality by reconstructing multiple slices jointly with low-rank tensor completion. Specifically, the multichannel k-space data from multiple slices are constructed into a block-wise Hankel tensor and iteratively updated by promoting tensor low-rankness through higher-order SVD. This multislice block-wise Hankel tensor completion was implemented for 2D spiral and Cartesian k-space undersampling where sampling patterns vary between adjacent slices. The approach was evaluated with human brain MR data and compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction.

RESULTS

The proposed multislice block-wise Hankel tensor completion approach robustly reconstructed highly undersampled multislice 2D spiral and Cartesian data. It produced substantially lower level of artifacts compared to the traditional single-slice simultaneous autocalibrating and k-space estimation reconstruction. Quantitative evaluation using error maps and root mean square error demonstrated its significantly improved performance in terms of residual artifacts and root mean square error.

CONCLUSION

Our proposed multislice block-wise Hankel tensor completion method exploits the similar coil sensitivity and image content within multislice MR data through a tensor completion framework. It offers a new and effective approach to acquire and reconstruct highly undersampled multislice MR data in a calibrationless manner.

High-dimensional embedding network derived prior for compressive sensing MRI reconstruction

Although recent deep learning methodology has shown promising performance in fast imaging, the network needs to be retrained for specific sampling patterns and ratios. Therefore, how to explore the network as a general prior and leverage it into the observation constraint flexibly is urgent. In this work, we present a multi-channel enhanced Deep Mean-Shift Prior (MEDMSP) to address the highly under-sampled magnetic resonance imaging reconstruction problem. By extending the naive DMSP via integration of multi-model aggregation and multi-channel network learning, a high-dimensional embedding network derived prior is formed. Then, we apply the learned prior to single-channel image reconstruction via variable augmentation technique. The resulting model is tackled by proximal gradient descent and alternative iteration. Experimental results under various sampling trajectories and acceleration factors consistently demonstrated the superiority of the proposed prior.

Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning

The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This paper focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

Improved MUSSELS reconstruction for high-resolution multi-shot diffusion weighted imaging

PURPOSE

MUSSELS is a one-step iterative reconstruction method for multishot diffusion weighted (msDW) imaging. The current work presents an efficient implementation, termed IRLS MUSSELS, that enables faster reconstruction to enhance its utility for high-resolution diffusion MRI studies.

METHODS

The recently proposed MUSSELS reconstruction belongs to a new class of parallel imaging-based methods that recover artifact-free DWIs from msDW data without needing phase compensation. The reconstruction is achieved via structured low-rank matrix completion algorithms, which are computationally demanding due to the large size of the Hankel matrices and their associated computations involving singular value decompositions. Because of this, computational demands of the MUSSELS reconstruction scales as the matrix size and the number of shots increases, which hinders its practical utility for high-resolution applications. In this work, we derive a computationally efficient MUSSELS formulation by modifying the iterative reweighted least squares (IRLS) method that were proposed earlier to solve such problems. Using whole-brain in vivo data, we show the utility of the IRLS MUSSELS for routine high-resolution studies with reduced computational burden.

RESULTS

IRLS MUSSELS provides about five times faster reconstruction for matrix sizes 192 × 192 and 256 × 256 compared to the earlier MUSSELS implementation. The widely employed conjugate symmetry priors can also be incorporated into IRLS MUSSELS to reduce blurring of the partial Fourier acquisitions, without incurring much computational burden.

CONCLUSIONS

The proposed method is observed to be computationally efficient to enable routine high-resolution studies. The computational complexity matches the traditional msDWI reconstruction methods and provides improved reconstruction results with the additional constraints.

Quantitative susceptibility map reconstruction using annihilating filter-based low-rank Hankel matrix approach

PURPOSE

Quantitative susceptibility mapping (QSM) inevitably suffers from streaking artifacts caused by zeros on the conical surface of the dipole kernel in k-space. This work proposes a novel and accurate QSM reconstruction method based on k-space low-rank Hankel matrix constraint, avoiding the over-smoothing problem and streaking artifacts.

THEORY AND METHODS

Based on the recent theory of annihilating filter-based low-rank Hankel matrix approach (ALOHA), QSM is formulated as deconvolution under low-rank Hankel matrix constraint in the k-space. The computational complexity and the high memory burden were reduced by successive reconstruction of 2-D planes along 3 independent axes of the 3-D phase image in Fourier domain. Feasibility of the proposed method was tested on a simulated phantom and human data and were compared with existing QSM reconstruction methods.

RESULTS

The proposed ALOHA-QSM effectively reduced streaking artifacts and accurately estimated susceptibility values in deep gray matter structures, compared to the existing QSM methods.

CONCLUSIONS

The suggested ALOHA-QSM algorithm successfully solves the 3-dimensional QSM dipole inversion problem using k-space low rank property with no anatomical constraint. ALOHA-QSM can provide detailed brain structures and accurate susceptibility values with no streaking artifacts.

k-Space deep learning for reference-free EPI ghost correction

PURPOSE

Nyquist ghost artifacts in echo planar imaging (EPI) are originated from phase mismatch between the even and odd echoes. However, conventional correction methods using reference scans often produce erroneous results especially in high-field MRI due to the nonlinear and time-varying local magnetic field changes. Recently, it was shown that the problem of ghost correction can be reformulated as k-space interpolation problem that can be solved using structured low-rank Hankel matrix approaches. Another recent work showed that data driven Hankel matrix decomposition can be reformulated to exhibit similar structures as deep convolutional neural network. By synergistically combining these findings, we propose a k-space deep learning approach that immediately corrects the phase mismatch without a reference scan in both accelerated and non-accelerated EPI acquisitions.

THEORY AND METHODS

To take advantage of the even and odd-phase directional redundancy, the k-space data are divided into 2 channels configured with even and odd phase encodings. The redundancies between coils are also exploited by stacking the multi-coil k-space data into additional input channels. Then, our k-space ghost correction network is trained to learn the interpolation kernel to estimate the missing virtual k-space data. For the accelerated EPI data, the same neural network is trained to directly estimate the interpolation kernels for missing k-space data from both ghost and subsampling.

RESULTS

Reconstruction results using 3T and 7T in vivo data showed that the proposed method outperformed the image quality compared to the existing methods, and the computing time is much faster.

CONCLUSIONS

The proposed k-space deep learning for EPI ghost correction is highly robust and fast, and can be combined with acceleration, so that it can be used as a promising correction tool for high-field MRI without changing the current acquisition protocol.

Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery

We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.

The quest for high spatial resolution diffusion-weighted imaging of the human brain in vivo

Diffusion-weighted imaging, a contrast unique to MRI, is used for assessment of tissue microstructure in vivo. However, this exquisite sensitivity to finer scales far above imaging resolution comes at the cost of vulnerability to errors caused by sources of motion other than diffusion motion. Addressing the issue of motion has traditionally limited diffusion-weighted imaging to a few acquisition techniques and, as a consequence, to poorer spatial resolution than other MRI applications. Advances in MRI imaging methodology have allowed diffusion-weighted MRI to push to ever higher spatial resolution. In this review we focus on the pulse sequences and associated techniques under development that have pushed the limits of image quality and spatial resolution in diffusion-weighted MRI.

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.

Nyquist ghost correction of breast diffusion weighted imaging using referenceless methods

PURPOSE

Correction of Nyquist ghosts for single-shot spin-echo EPI using the standard 3-line navigator often fails in breast DWI because of incomplete fat suppression, respiration, and greater B₀ inhomogeneity. The purpose of this work is to compare the performance of the 3-line navigator with 4 data-driven methods termed "referenceless methods," including 2 previously proposed in literature, 1 introduced in this work, and finally a combination of all 3, in breast DWI.

METHODS

Breast DWI was acquired for 41 patients with SS SE-EPI. Raw data was corrected offline with the standard 3-line navigator and 4 referenceless methods, which modeled the ghost as a linear phase error and minimized 3 unique cost functions as well as the median solution of all 3. Ghost levels were evaluated based on the signal intensity in the background region, defined by a mask auto-generated from a T₁ -weighted anatomical image. Ghost intensity measurements were fit to a linear mixed model including ghost correction method and b-value as covariates.

RESULTS

All 4 referenceless methods outperformed the standard 3-line navigator with statistical significance at all 4 b-values tested (b = 0, 100, 600, and 800 s/mm² ).

CONCLUSIONS

Referenceless methods provide a robust way to reduce Nyquist ghosts in breast DWI without the need for any additional calibration scan.

Navigator-Free EPI Ghost Correction With Structured Low-Rank Matrix Models: New Theory and Methods

Structured low-rank matrix models have previously been introduced to enable calibrationless MR image reconstruction from sub-Nyquist data, and such ideas have recently been extended to enable navigator-free echo-planar imaging (EPI) ghost correction. This paper presents a novel theoretical analysis which shows that, because of uniform subsampling, the structured low-rank matrix optimization problems for EPI data will always have either undesirable or non-unique solutions in the absence of additional constraints. This theory leads us to recommend and investigate problem formulations for navigator-free EPI that incorporate side information from either image-domain or k-space domain parallel imaging methods. The importance of using nonconvex low-rank matrix regularization is also identified. We demonstrate using phantom and in vivo data that the proposed methods are able to eliminate ghost artifacts for several navigator-free EPI acquisition schemes, obtaining better performance in comparison with the state-of-the-art methods across a range of different scenarios. Results are shown for both single-channel acquisition and highly accelerated multi-channel acquisition.

Improving parallel imaging by jointly reconstructing multi-contrast data

PURPOSE

To develop parallel imaging techniques that simultaneously exploit coil sensitivity encoding, image phase prior information, similarities across multiple images, and complementary k-space sampling for highly accelerated data acquisition.

METHODS

We introduce joint virtual coil (JVC)-generalized autocalibrating partially parallel acquisitions (GRAPPA) to jointly reconstruct data acquired with different contrast preparations, and show its application in 2D, 3D, and simultaneous multi-slice (SMS) acquisitions. We extend the joint parallel imaging concept to exploit limited support and smooth phase constraints through Joint (J-) LORAKS formulation. J-LORAKS allows joint parallel imaging from limited autocalibration signal region, as well as permitting partial Fourier sampling and calibrationless reconstruction.

RESULTS

We demonstrate highly accelerated 2D balanced steady-state free precession with phase cycling, SMS multi-echo spin echo, 3D multi-echo magnetization-prepared rapid gradient echo, and multi-echo gradient recalled echo acquisitions in vivo. Compared to conventional GRAPPA, proposed joint acquisition/reconstruction techniques provide more than 2-fold reduction in reconstruction error.

CONCLUSION

JVC-GRAPPA takes advantage of additional spatial encoding from phase information and image similarity, and employs different sampling patterns across acquisitions. J-LORAKS achieves a more parsimonious low-rank representation of local k-space by considering multiple images as additional coils. Both approaches provide dramatic improvement in artifact and noise mitigation over conventional single-contrast parallel imaging reconstruction. Magn Reson Med 80:619-632, 2018. © 2018 International Society for Magnetic Resonance in Medicine.

Grid-Free Localization Algorithm Using Low-rank Hankel Matrix for Super-Resolution Microscopy

Localization microscopy, such as STORM / PALM, can reconstruct super-resolution images with a nanometer resolution through the iterative localization of fluorescence molecules. Recent studies in this area have focused mainly on the localization of densely activated molecules to improve temporal resolutions. However, higher density imaging requires an advanced algorithm that can resolve closely spaced molecules. Accordingly, sparsitydriven methods have been studied extensively. One of the major limitations of existing sparsity-driven approaches is the need for a fine sampling grid or for Taylor series approximation which may result in some degree of localization bias toward the grid. In addition, prior knowledge of the point-spread function (PSF) is required. To address these drawbacks, here we propose a true grid-free localization algorithm with adaptive PSF estimation. Specifically, based on the observation that sparsity in the spatial domain implies a low rank in the Fourier domain, the proposed method converts source localization problems into Fourier-domain signal processing problems so that a truly gridfree localization is possible. We verify the performance of the newly proposed method with several numerical simulations and a live-cell imaging experiment.

Ghost reduction in echo-planar imaging by joint reconstruction of images and line-to-line delays and phase errors

PURPOSE

To correct line-to-line delays and phase errors in echo-planar imaging (EPI).

THEORY AND METHODS

EPI-trajectory auto-corrected image reconstruction (EPI-TrACR) is an iterative maximum-likelihood technique that exploits data redundancy provided by multiple receive coils between nearby lines of k-space to determine and correct line-to-line trajectory delays and phase errors that cause ghosting artifacts. EPI-TrACR was efficiently implemented using a segmented FFT and was applied to in vivo brain data acquired at 7 T across acceleration (1×-4×) and multishot factors (1-4 shots), and in a time series.

RESULTS

EPI-TrACR reduced ghosting across all acceleration factors and multishot factors, compared to conventional calibrated reconstructions and the PAGE method. It also achieved consistently lower ghosting in the time series. Averaged over all cases, EPI-TrACR reduced root-mean-square ghosted signal outside the brain by 27% compared to calibrated reconstruction, and by 40% compared to PAGE.

CONCLUSION

EPI-TrACR automatically corrects line-to-line delays and phase errors in multishot, accelerated, and dynamic EPI. While the method benefits from additional calibration data for initialization, it was not a requirement for most reconstructions. Magn Reson Med 79:3114-3121, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Framing U-Net via Deep Convolutional Framelets: Application to Sparse-View CT

X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse-view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U-Net variants such as dual frame and tight frame U-Nets satisfy the so-called frame condition which makes them better for effective recovery of high frequency edges in sparse-view CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance.

ROBUST AUTOCALIBRATED LORAKS FOR EPI GHOST CORRECTION

Nyquist ghosts are a longstanding problem in a variety of fast MRI experiments that use echo-planar imaging (EPI). Recently, several structured low-rank matrix modeling approaches have been proposed that achieve state-of-the-art ghost-elimination, although the performance of these approaches is still inadequate in several important scenarios. We present a new structured low-rank matrix recovery ghost correction method that we call Robust Autocalibrated LORAKS (RAC-LORAKS). RAC-LORAKS incorporates constraints from autocalibration data to avoid ill-posedness, but allows adaptation of these constraints to gain robustness against possible autocalibration imperfections. RAC-LORAKS is tested in two challenging scenarios: highly-undersampled multi-channel EPI of the brain, and cardiac EPI with a double-oblique slice orientation. Results show that RAC-LORAKS can provide substantial improvements over existing ghost correction methods, and potentially enables new imaging applications that were previously confounded by ghost artifacts.

Deep Residual Learning for Accelerated MRI Using Magnitude and Phase Networks

OBJECTIVE

Accelerated magnetic resonance (MR) image acquisition with compressed sensing (CS) and parallel imaging is a powerful method to reduce MR imaging scan time. However, many reconstruction algorithms have high computational costs. To address this, we investigate deep residual learning networks to remove aliasing artifacts from artifact corrupted images.

METHODS

The deep residual learning networks are composed of magnitude and phase networks that are separately trained. If both phase and magnitude information are available, the proposed algorithm can work as an iterative k-space interpolation algorithm using framelet representation. When only magnitude data are available, the proposed approach works as an image domain postprocessing algorithm.

RESULTS

Even with strong coherent aliasing artifacts, the proposed network successfully learned and removed the aliasing artifacts, whereas current parallel and CS reconstruction methods were unable to remove these artifacts.

CONCLUSION

Comparisons using single and multiple coil acquisition show that the proposed residual network provides good reconstruction results with orders of magnitude faster computational time than existing CS methods.

SIGNIFICANCE

The proposed deep learning framework may have a great potential for accelerated MR reconstruction by generating accurate results immediately.

DENOISING AND DEINTERLEAVING OF EPSI DATA USING STRUCTURED LOW-RANK MATRIX RECOVERY

Echo-planar spectroscopic imaging (EPSI) sequence with spectrally interleaving is often used to rapidly collect metabolic MRI data. The main problem in using it on high field scanners is the presence of spurious peaks resulting from phase distortions between interleaves as well as the low signal to noise ratio. We introduce a novel structured low-rank framework for the simultaneous denoising and deinterleaving of spectrally interleaved EPSI data. The proposed algorithm exploits annihilation relations resulting from the linear predicability of exponential signals as well as due to uncorrected phase relations between interleaves. The algorithm is formulated as a structured nuclear norm minimization of a block Hankel matrix, derived from the interleaves. Experiments using hyperpolarized 13 C mouse kidney EPSI data demonstrate the ability of the algorithm to remove ghost peaks from EPSI data collected using bipolar readout gradients.

Sparse and Low-Rank Decomposition of a Hankel Structured Matrix for Impulse Noise Removal

Recently, the annihilating filter-based low-rank Hankel matrix (ALOHA) approach was proposed as a powerful image inpainting method. Based on the observation that smoothness or textures within an image patch correspond to sparse spectral components in the frequency domain, ALOHA exploits the existence of annihilating filters and the associated rank-deficient Hankel matrices in an image domain to estimate any missing pixels. By extending this idea, we propose a novel impulse-noise removal algorithm that uses the sparse and low-rank decomposition of a Hankel structured matrix. This method, referred to as the robust ALOHA, is based on the observation that an image corrupted with the impulse noise has intact pixels; consequently, the impulse noise can be modeled as sparse components, whereas the underlying image can still be modeled using a low-rank Hankel structured matrix. To solve the sparse and low-rank matrix decomposition problem, we propose an alternating direction method of multiplier approach, with initial factorized matrices coming from a low-rank matrix-fitting algorithm. To adapt local image statistics that have distinct spectral distributions, the robust ALOHA is applied in a patch-by-patch manner. Experimental results from impulse noise for both single-channel and multichannel color images demonstrate that the robust ALOHA is superior to existing approaches, especially during the reconstruction of complex texture patterns.

A general algorithm for compensation of trajectory errors: Application to radial imaging

PURPOSE

To reconstruct artifact-free images from measured k-space data, when the actual k-space trajectory deviates from the nominal trajectory due to gradient imperfections.

METHODS

Trajectory errors arising from eddy currents and gradient delays introduce phase inconsistencies in several fast scanning MR pulse sequences, resulting in image artifacts. The proposed algorithm provides a novel framework to compensate for this phase distortion. The algorithm relies on the construction of a multi-block Hankel matrix, where each block is constructed from k-space segments with the same phase distortion. In the presence of spatially smooth phase distortions between the segments, the complete block-Hankel matrix is known to be highly low-rank. Since each k-space segment is only acquiring part of the k-space data, the reconstruction of the phase compensated image from their partially parallel measurements is posed as a structured low-rank matrix optimization problem, assuming the coil sensitivities to be known.

RESULTS

The proposed formulation is tested on radial acquisitions in several settings including partial Fourier and golden-angle acquisitions. The experiments demonstrate the ability of the algorithm to successfully remove the artifacts arising from the trajectory errors, without the need for trajectory or phase calibration. The quality of the reconstruction was comparable to corrections achieved using the Trajectory Auto-Corrected Image Reconstruction (TrACR) for radial acquisitions.

CONCLUSION

The proposed method provides a general framework for the recovery of artifact-free images from radial trajectories without the need for trajectory calibration.

A Fast Algorithm for Convolutional Structured Low-rank Matrix Recovery

Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multi-level generalizations, built from Fourier data of the image should be low-rank. The main challenge in applying these schemes to large-scale problems is the computational complexity and memory demand resulting from a lifting the image data to a large scale matrix. We introduce a fast and memory efficient approach called the Generic Iterative Reweighted Annihilation Filter (GIRAF) algorithm that exploits the convolutional structure of the lifted matrix to work in the original un-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of images from undersampled Fourier measurements show that the resulting algorithm is considerably faster than previously proposed algorithms, and can accommodate much larger problem sizes than previously studied.

Multi-shot sensitivity-encoded diffusion data recovery using structured low-rank matrix completion (MUSSELS)

PURPOSE

To introduce a novel method for the recovery of multi-shot diffusion weighted (MS-DW) images from echo-planar imaging (EPI) acquisitions.

METHODS

Current EPI-based MS-DW reconstruction methods rely on the explicit estimation of the motion-induced phase maps to recover artifact-free images. In the new formulation, the k-space data of the artifact-free DWI is recovered using a structured low-rank matrix completion scheme, which does not require explicit estimation of the phase maps. The structured matrix is obtained as the lifting of the multi-shot data. The smooth phase-modulations between shots manifest as null-space vectors of this matrix, which implies that the structured matrix is low-rank. The missing entries of the structured matrix are filled in using a nuclear-norm minimization algorithm subject to the data-consistency. The formulation enables the natural introduction of smoothness regularization, thus enabling implicit motion-compensated recovery of the MS-DW data.

RESULTS

Our experiments on in-vivo data show effective removal of artifacts arising from inter-shot motion using the proposed method. The method is shown to achieve better reconstruction than the conventional phase-based methods.

CONCLUSION

We demonstrate the utility of the proposed method to effectively recover artifact-free images from Cartesian fully/under-sampled and partial Fourier acquired data without the use of explicit phase estimates. Magn Reson Med 78:494-507, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Comprehensive reconstruction of multi-shot multi-channel diffusion data using mussels

Echo planar imaging (EPI)-based magnetic resonance imaging (MRI) data are often corrupted by Nyquist ghost artifacts resulting from odd-even shifts of the EPI read-outs. Algorithms that corrects for the Nyquist ghost artifacts rely on calibration scans that are collected prior to the data acquisition. However, a more complex pattern of ghosting artifacts arises when diffusion-weighted data are acquired using segmented k-space EPI read-outs. The additional under-sampling present in the segmented acquisitions and the inter-shot motion during diffusion weighted acquistion cause ghosting artifacts in addition to the EPI ghosting arising from odd-even shifts. We propose a comprehensive method that can remove the Nyquist-ghosting artifacts as well as the inter-shot motion-induced ghosting artifacts in diffusion weighted images in a single step from partial Fourier data without the need for a calibration scan. We show very high quality diffusion data recovery using the proposed method.

MRI artifact correction using sparse + low-rank decomposition of annihilating filter-based hankel matrix

PURPOSE

Magnetic resonance imaging (MRI) artifacts are originated from various sources including instability of an magnetic resonance (MR) system, patient motion, inhomogeneities of gradient fields, and so on. Such MRI artifacts are usually considered as irreversible, so additional artifact-free scan or navigator scan is necessary. To overcome these limitations, this article proposes a novel compressed sensing-based approach for removal of various MRI artifacts.

THEORY

Recently, the annihilating filter based low-rank Hankel matrix approach was proposed. The annihilating filter based low-rank Hankel matrix exploits the duality between the low-rankness of weighted Hankel structured matrix and the sparsity of signal in a transform domain. Because MR artifacts usually appeared as sparse k-space components, the low-rank Hankel matrix from underlying artifact-free k-space data can be exploited to decompose the sparse outliers.

METHODS

The sparse + low-rank decomposition framework using Hankel matrix was proposed for removal of MRI artifacts. Alternating direction method of multipliers algorithm was employed for the minimization of associated cost function with the initialized matrices from a factorization-based matrix completion.

RESULTS

Experimental results demonstrated that the proposed algorithm can correct MR artifacts including herringbone (crisscross), motion, and zipper artifacts without image distortion.

CONCLUSION

The proposed method may be a robust correction solution for various MRI artifacts that can be represented as sparse outliers. Magn Reson Med 78:327-340, 2017. © 2016 International Society for Magnetic Resonance in Medicine.