SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space

Nonlocal transform-domain filter for volumetric data denoising and reconstruction

We present an extension of the BM3D filter to volumetric data. The proposed algorithm, BM4D, implements the grouping and collaborative filtering paradigm, where mutually similar d-dimensional patches are stacked together in a (d+1)-dimensional array and jointly filtered in transform domain. While in BM3D the basic data patches are blocks of pixels, in BM4D we utilize cubes of voxels, which are stacked into a 4-D "group." The 4-D transform applied on the group simultaneously exploits the local correlation present among voxels in each cube and the nonlocal correlation between the corresponding voxels of different cubes. Thus, the spectrum of the group is highly sparse, leading to very effective separation of signal and noise through coefficient shrinkage. After inverse transformation, we obtain estimates of each grouped cube, which are then adaptively aggregated at their original locations. We evaluate the algorithm on denoising of volumetric data corrupted by Gaussian and Rician noise, as well as on reconstruction of volumetric phantom data with non-zero phase from noisy and incomplete Fourier-domain (k-space) measurements. Experimental results demonstrate the state-of-the-art denoising performance of BM4D, and its effectiveness when exploited as a regularizer in volumetric data reconstruction.

Compressive sensing with dispersion compensation on non-linear wavenumber sampled spectral domain optical coherence tomography

We propose a novel compressive sensing (CS) method on spectral domain optical coherence tomography (SDOCT). By replacing the widely used uniform discrete Fourier transform (UDFT) matrix with a new sensing matrix which is a modification of the non-uniform discrete Fourier transform (NUDFT) matrix, it is shown that undersampled non-linear wavenumber spectral data can be used directly in the CS reconstruction. Thus k-space grid filling and k-linear mask calibration which were proposed to obtain linear wavenumber sampling from the non-linear wavenumber interferometric spectra in previous studies of CS in SDOCT (CS-SDOCT) are no longer needed. The NUDFT matrix is modified to promote the sparsity of reconstructed A-scans by making them symmetric while preserving the value of the desired half. In addition, we show that dispersion compensation can be implemented by multiplying the frequency-dependent correcting phase directly to the real spectra, eliminating the need for constructing complex component of the real spectra. This enables the incorporation of dispersion compensation into the CS reconstruction by adding the correcting term to the modified NUDFT matrix. With this new sensing matrix, A-scan with dispersion compensation can be reconstructed from undersampled non-linear wavenumber spectral data by CS reconstruction. Experimental results show that proposed method can achieve high quality imaging with dispersion compensation.

Compressed-sensing multispectral imaging of the postoperative spine

PURPOSE

To apply compressed sensing (CS) to in vivo multispectral imaging (MSI), which uses additional encoding to avoid magnetic resonance imaging (MRI) artifacts near metal, and demonstrate the feasibility of CS-MSI in postoperative spinal imaging.

MATERIALS AND METHODS

Thirteen subjects referred for spinal MRI were examined using T2-weighted MSI. A CS undersampling factor was first determined using a structural similarity index as a metric for image quality. Next, these fully sampled datasets were retrospectively undersampled using a variable-density random sampling scheme and reconstructed using an iterative soft-thresholding method. The fully and undersampled images were compared using a 5-point scale. Prospectively undersampled CS-MSI data were also acquired from two subjects to ensure that the prospective random sampling did not affect the image quality.

RESULTS

A two-fold outer reduction factor was deemed feasible for the spinal datasets. CS-MSI images were shown to be equivalent or better than the original MSI images in all categories: nerve visualization: P = 0.00018; image artifact: P = 0.00031; image quality: P = 0.0030. No alteration of image quality and T2 contrast was observed from prospectively undersampled CS-MSI.

CONCLUSION

This study shows that the inherently sparse nature of MSI data allows modest undersampling followed by CS reconstruction with no loss of diagnostic quality.

Nonlinear coil sensitivity estimation for parallel magnetic resonance imaging using data-adaptive steering kernel regression method

The parallel magnetic resonance imaging (parallel imaging) technique reduces the MR data acquisition time by using multiple receiver coils. Coil sensitivity estimation is critical for the performance of parallel imaging reconstruction. Currently, most coil sensitivity estimation methods are based on linear interpolation techniques. Such methods may result in Gibbs-ringing artifact or resolution loss, when the resolution of coil sensitivity data is limited. To solve the problem, we proposed a nonlinear coil sensitivity estimation method based on steering kernel regression, which performs a local gradient guided interpolation to the coil sensitivity. The in vivo experimental results demonstrate that this method can effectively suppress Gibbs ringing artifact in coil sensitivity and reduces both noise and residual aliasing artifact level in SENSE reconstruction.

A simple application of compressed sensing to further accelerate partially parallel imaging

Compressed sensing (CS) and partially parallel imaging (PPI) enable fast magnetic resonance (MR) imaging by reducing the amount of k-space data required for reconstruction. Past attempts to combine these two have been limited by the incoherent sampling requirement of CS since PPI routines typically sample on a regular (coherent) grid. Here, we developed a new method, "CS+GRAPPA," to overcome this limitation. We decomposed sets of equidistant samples into multiple random subsets. Then, we reconstructed each subset using CS and averaged the results to get a final CS k-space reconstruction. We used both a standard CS and an edge- and joint-sparsity-guided CS reconstruction. We tested these intermediate results on both synthetic and real MR phantom data and performed a human observer experiment to determine the effectiveness of decomposition and to optimize the number of subsets. We then used these CS reconstructions to calibrate the generalized autocalibrating partially parallel acquisitions (GRAPPA) complex coil weights. In vivo parallel MR brain and heart data sets were used. An objective image quality evaluation metric, Case-PDM, was used to quantify image quality. Coherent aliasing and noise artifacts were significantly reduced using two decompositions. More decompositions further reduced coherent aliasing and noise artifacts but introduced blurring. However, the blurring was effectively minimized using our new edge- and joint-sparsity-guided CS using two decompositions. Numerical results on parallel data demonstrated that the combined method greatly improved image quality as compared to standard GRAPPA, on average halving Case-PDM scores across a range of sampling rates. The proposed technique allowed the same Case-PDM scores as standard GRAPPA using about half the number of samples. We conclude that the new method augments GRAPPA by combining it with CS, allowing CS to work even when the k-space sampling pattern is equidistant.

SC-GRAPPA: Self-constraint noniterative GRAPPA reconstruction with closed-form solution

PURPOSE

Parallel MRI (pMRI) reconstruction techniques are commonly used to reduce scan time by undersampling the k-space data. GRAPPA, a k-space based pMRI technique, is widely used clinically because of its robustness. In GRAPPA, the missing k-space data are estimated by solving a set of linear equations; however, this set of equations does not take advantage of the correlations within the missing k-space data. All k-space data in a neighborhood acquired from a phased-array coil are correlated. The correlation can be estimated easily as a self-constraint condition, and formulated as an extra set of linear equations to improve the performance of GRAPPA. The authors propose a modified k-space based pMRI technique called self-constraint GRAPPA (SC-GRAPPA) which combines the linear equations of GRAPPA with these extra equations to solve for the missing k-space data. Since SC-GRAPPA utilizes a least-squares solution of the linear equations, it has a closed-form solution that does not require an iterative solver.

METHODS

The SC-GRAPPA equation was derived by incorporating GRAPPA as a prior estimate. SC-GRAPPA was tested in a uniform phantom and two normal volunteers. MR real-time cardiac cine images with acceleration rate 5 and 6 were reconstructed using GRAPPA and SC-GRAPPA.

RESULTS

SC-GRAPPA showed a significantly lower artifact level, and a greater than 10% overall signal-to-noise ratio (SNR) gain over GRAPPA, with more significant SNR gain observed in low-SNR regions of the images.

CONCLUSIONS

SC-GRAPPA offers improved pMRI reconstruction, and is expected to benefit clinical imaging applications in the future.

Correlation imaging for multiscan MRI with parallel data acquisition

A new approach to high-speed magnetic resonance imaging (MRI) that uses all the data acquired in a multiscan imaging session is presented. This approach accelerates MRI data acquisition by statistically estimating correlation functions from images with different contrast and/or resolution. In multiscan MRI with parallel data acquisition, the estimation of correlation functions is dynamically improved as imaging proceeds. This allows imaging acceleration factors to be increased in subsequent scans, thereby reducing the total time of a multiscan MRI protocol. Furthermore, the correlation function estimates bring information about both coil sensitivity and anatomical structure into image reconstruction, thereby offering the ability to speed up MRI beyond the parallel imaging acceleration limit posed by a coil array alone. In this study, the feasibility of correlation imaging is demonstrated experimentally using brain and spine imaging protocols. The ability of correlation imaging to achieve an aggregate acceleration factor in excess of the number of coil elements in the phase encoding direction is also demonstrated.

Venous and arterial flow quantification are equally accurate and precise with parallel imaging compressed sensing 4D phase contrast MRI

PURPOSE

To evaluate the precision and accuracy of parallel-imaging compressed-sensing 4D phase contrast (PICS-4DPC) magnetic resonance imaging (MRI) venous flow quantification in children with patients referred for cardiac MRI at our children's hospital.

MATERIALS AND METHODS

With Institutional Review Board (IRB) approval and Health Insurance Portability and Accountability Act (HIPAA) compliance, 22 consecutive patients without shunts underwent 4DPC as part of clinical cardiac MRI examinations. Flow measurements were obtained in the superior and inferior vena cava, ascending and descending aorta, and the pulmonary trunk. Conservation of flow to the upper, lower, and whole body was used as an internal physiologic control. The arterial and venous flow rates at each location were compared with paired t-tests and F-tests to assess relative accuracy and precision.

RESULTS

Arterial and venous flow measurements were strongly correlated with the upper (ρ = 0.89), lower (ρ = 0.96), and whole body (ρ = 0.97); net aortic and pulmonary trunk flow rates were also tightly correlated (ρ = 0.97). There was no significant difference in the value or precision of arterial and venous flow measurements in upper, lower, or whole body, although there was a trend toward improved precision with lower velocity-encoding settings.

CONCLUSION

With PICS-4DPC MRI, the accuracy and precision of venous flow quantification are comparable to that of arterial flow quantification at velocity-encodings appropriate for arterial vessels.

32-channel phased-array receive with asymmetric birdcage transmit coil for hyperpolarized xenon-129 lung imaging

Hyperpolarized xenon-129 has the potential to become a noninvasive contrast agent for lung MRI. In addition to its utility for imaging of ventilated airspaces, the property of xenon to dissolve in lung tissue and blood upon inhalation provides the opportunity to study gas exchange. Implementations of imaging protocols for obtaining regional parameters that exploit the dissolved phase are limited by the available signal-to-noise ratio, excitation homogeneity, and length of acquisition times. To address these challenges, a 32-channel receive-array coil complemented by an asymmetric birdcage transmit coil tuned to the hyperpolarized xenon-129 resonance at 3 T was developed. First results of spin-density imaging in healthy subjects and subjects with obstructive lung disease demonstrated the improvements in image quality by high-resolution ventilation images with high signal-to-noise ratio. Parallel imaging performance of the phased-array coil was demonstrated by acceleration factors up to three in 2D acquisitions and up to six in 3D acquisitions. Transmit-field maps showed a regional variation of only 8% across the whole lung. The newly developed phased-array receive coil with the birdcage transmit coil will lead to an improvement in existing imaging protocols, but moreover enable the development of new, functional lung imaging protocols based on the improvements in excitation homogeneity, signal-to-noise ratio, and acquisition speed.

Evaluation of partial k-space strategies to speed up time-domain EPR imaging

Narrow-line spin probes derived from the trityl radical have led to the development of fast in vivo time-domain EPR imaging. Pure phase-encoding imaging modalities based on the single-point imaging scheme have demonstrated the feasibility of three-dimensional oximetric images with functional information in minutes. In this article, we explore techniques to improve the temporal resolution and circumvent the relatively short biological half-lives of trityl probes using partial k-space strategies. There are two main approaches: one involves the use of the Hermitian character of the k-space by which only part of the k-space is measured and the unmeasured part is generated using the Hermitian symmetry. This approach is limited in success by the accuracy of numerical estimate of the phase roll in the k-space that corrupts the Hermiticy. The other approach is to measure only a judicially chosen reduced region of k-space (a centrosymmetric ellipsoid region) that more or less accounts for >70% of the k-space energy. Both of these aspects were explored in Fourier transform-EPR imaging with a doubling of scan speed demonstrated by considering ellipsoid geometry of the k-space. Partial k-space strategies help improve the temporal resolution in studying fast dynamics of functional aspects in vivo with infused spin probes.

The Role of Nonlinear Gradients in Parallel Imaging: A k-Space Based Analysis

Sequences that encode the spatial information of an object using nonlinear gradient fields are a new frontier in MRI, with potential to provide lower peripheral nerve stimulation, windowed fields of view, tailored spatially-varying resolution, curved slices that mirror physiological geometry, and, most importantly, very fast parallel imaging with multichannel coils. The acceleration for multichannel images is generally explained by the fact that curvilinear gradient isocontours better complement the azimuthal spatial encoding provided by typical receiver arrays. However, the details of this complementarity have been more difficult to specify. We present a simple and intuitive framework for describing the mechanics of image formation with nonlinear gradients, and we use this framework to review some the main classes of nonlinear encoding schemes.

Evaluation of valvular insufficiency and shunts with parallel-imaging compressed-sensing 4D phase-contrast MR imaging with stereoscopic 3D velocity-fusion volume-rendered visualization

PURPOSE

To assess the potential of compressed-sensing parallel-imaging four-dimensional (4D) phase-contrast magnetic resonance (MR) imaging and specialized imaging software in the evaluation of valvular insufficiency and intracardiac shunts in patients with congenital heart disease.

MATERIALS AND METHODS

Institutional review board approval was obtained for this HIPAA-compliant study. Thirty-four consecutive retrospectively identified patients in whom a compressed-sensing parallel-imaging 4D phase-contrast sequence was performed as part of routine clinical cardiac MR imaging between March 2010 and August 2011 and who had undergone echocardiography were included. Multiplanar, volume-rendered, and stereoscopic three-dimensional velocity-fusion visualization algorithms were developed and implemented in Java and OpenGL. Two radiologists independently reviewed 4D phase-contrast studies for each of 34 patients (mean age, 6 years; age range, 10 months to 21 years) and tabulated visible shunts and valvular regurgitation. These results were compared with color Doppler echocardiographic and cardiac MR imaging reports, which were generated without 4D phase-contrast visualization. Cohen κ statistics were computed to assess interobserver agreement and agreement with echocardiographic results.

RESULTS

The 4D phase-contrast acquisitions were performed, on average, in less than 10 minutes. Among 123 valves seen in 34 4D phase-contrast studies, 29 regurgitant valves were identified, with good agreement between observers (k=0.85). There was also good agreement with the presence of at least mild regurgitation at echocardiography (observer 1, κ=0.76; observer 2, κ=0.77) with high sensitivity (observer 1, 75%; observer 2, 82%) and specificity (observer 1, 97%; observer 2, 95%) relative to the reference standard. Eight intracardiac shunts were identified, four of which were not visible with conventional cardiac MR imaging but were detected with echocardiography. No intracardiac shunts were found with echocardiography alone.

CONCLUSION

With velocity-fusion visualization, the compressed-sensing parallel-imaging 4D phase-contrast sequence can augment conventional cardiac MR imaging by improving sensitivity for and depiction of hemodynamically significant shunts and valvular regurgitation.

SENSE with improved tolerance to inaccuracies in coil sensitivity maps

In this work, an extension of the Cartesian sensitivity encoding (SENSE) parallel imaging framework is proposed. In the well-known SENSE solution, the overdetermined reconstruction inversion problem is optimized to get the highest signal-to-noise ratio in the image. In this extension, the probability of artifacts due to incorrect knowledge of the receiver coil sensitivities is also taken into account. This is realized by assuming an uncertainty in measured receiver coil sensitivities to enable weighting of residual artifact level and signal-to-noise ratio in the inversion problem. This inversion problem can still be solved by a least-squares optimization without the need of any complex iterative scheme. Results in abdominal imaging show that artifact levels can be substantially reduced, at the cost of a signal-to-noise ratio penalty. The size of the signal-to-noise ratio penalty depends on the assumed inaccuracy of the coil sensitivities, sensitivity encoding acceleration factor, and coil configuration.

Reconstruction of undersampled radial PatLoc imaging using total generalized variation

In the case of radial imaging with nonlinear spatial encoding fields, a prominent star-shaped artifact has been observed if a spin distribution is encoded with an undersampled trajectory. This work presents a new iterative reconstruction method based on the total generalized variation, which reduces this artifact. For this approach, a sampling operator (as well as its adjoint) is needed that maps data from PatLoc k-space to the final image space. It is shown that this can be realized as a type-3 nonuniform fast Fourier transform, which is implemented by a combination of a type-1 and type-2 nonuniform fast Fourier transform. Using this operator, it is also possible to implement an iterative conjugate gradient SENSE based method for PatLoc reconstruction, which leads to a significant reduction of computation time in comparison to conventional PatLoc image reconstruction methods. Results from numerical simulations and in vivo PatLoc measurements with as few as 16 radial projections are presented, which demonstrate significant improvements in image quality with the total generalized variation-based approach.

Accelerated 3D MERGE carotid imaging using compressed sensing with a hidden Markov tree model

PURPOSE

To determine the potential for accelerated 3D carotid magnetic resonance imaging (MRI) using wavelet based compressed sensing (CS) with a hidden Markov tree (HMT) model.

MATERIALS AND METHODS

We retrospectively applied HMT model-based CS and conventional CS to 3D carotid MRI data with 0.7 mm isotropic resolution from six subjects with known carotid stenosis (12 carotids). We applied a wavelet-tree model learned from a training database of carotid images to improve CS reconstruction. Quantitative endpoints such as lumen area, wall area, mean and maximum wall thickness, plaque calcification, and necrotic core area were measured and compared using Bland-Altman analysis along with image quality.

RESULTS

Rate-4.5 acceleration with HMT model-based CS provided image quality comparable to that of rate-3 acceleration with conventional CS and fully sampled reference reconstructions. Morphological measurements made on rate-4.5 HMT model-based CS reconstructions were in good agreement with measurements made on fully sampled reference images. There was no significant bias or correlation between mean and difference of measurements when comparing rate 4.5 HMT model-based CS with fully sampled reference images.

CONCLUSION

HMT model-based CS can potentially be used to accelerate clinical carotid MRI by a factor of 4.5 without impacting diagnostic quality or quantitative endpoints.

Sparse Methods for Biomedical Data

Following recent technological revolutions, the investigation of massive biomedical data with growing scale, diversity, and complexity has taken a center stage in modern data analysis. Although complex, the underlying representations of many biomedical data are often sparse. For example, for a certain disease such as leukemia, even though humans have tens of thousands of genes, only a few genes are relevant to the disease; a gene network is sparse since a regulatory pathway involves only a small number of genes; many biomedical signals are sparse or compressible in the sense that they have concise representations when expressed in a proper basis. Therefore, finding sparse representations is fundamentally important for scientific discovery. Sparse methods based on the [Formula: see text] norm have attracted a great amount of research efforts in the past decade due to its sparsity-inducing property, convenient convexity, and strong theoretical guarantees. They have achieved great success in various applications such as biomarker selection, biological network construction, and magnetic resonance imaging. In this paper, we review state-of-the-art sparse methods and their applications to biomedical data.

Fast l₁-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime

We present l₁-SPIRiT, a simple algorithm for auto calibrating parallel imaging (acPI) and compressed sensing (CS) that permits an efficient implementation with clinically-feasible runtimes. We propose a CS objective function that minimizes cross-channel joint sparsity in the wavelet domain. Our reconstruction minimizes this objective via iterative soft-thresholding, and integrates naturally with iterative self-consistent parallel imaging (SPIRiT). Like many iterative magnetic resonance imaging reconstructions, l₁-SPIRiT's image quality comes at a high computational cost. Excessively long runtimes are a barrier to the clinical use of any reconstruction approach, and thus we discuss our approach to efficiently parallelizing l₁-SPIRiT and to achieving clinically-feasible runtimes. We present parallelizations of l₁-SPIRiT for both multi-GPU systems and multi-core CPUs, and discuss the software optimization and parallelization decisions made in our implementation. The performance of these alternatives depends on the processor architecture, the size of the image matrix, and the number of parallel imaging channels. Fundamentally, achieving fast runtime requires the correct trade-off between cache usage and parallelization overheads. We demonstrate image quality via a case from our clinical experimentation, using a custom 3DFT spoiled gradient echo (SPGR) sequence with up to 8× acceleration via Poisson-disc undersampling in the two phase-encoded directions.

Free-breathing multiphase whole-heart coronary MR angiography using image-based navigators and three-dimensional cones imaging

Noninvasive visualization of the coronary arteries in vivo is one of the most important goals in cardiovascular imaging. Compared to other paradigms for coronary MR angiography, a free-breathing three-dimensional whole-heart iso-resolution approach simplifies prescription effort, requires less patient cooperation, reduces overall exam time, and supports retrospective reformats at arbitrary planes. However, this approach requires a long continuous acquisition and must account for respiratory and cardiac motion throughout the scan. In this work, a new free-breathing coronary MR angiography technique that reduces scan time and improves robustness to motion is developed. Data acquisition is accomplished using a three-dimensional cones non-Cartesian trajectory, which can reduce the number of readouts 3-fold or more compared to conventional three-dimensional Cartesian encoding and provides greater robustness to motion/flow effects. To further enhance robustness to motion, two-dimensional navigator images are acquired to directly track respiration-induced displacement of the heart and enable retrospective compensation of all acquired data (none discarded) for image reconstruction. In addition, multiple cardiac phases are imaged to support retrospective selection of the best phase(s) for visualizing each coronary segment. Experimental results demonstrate that whole-heart coronary angiograms can be obtained rapidly and robustly with this proposed technique.

Accelerated contrast-enhanced whole-heart coronary MRI using low-dimensional-structure self-learning and thresholding

We sought to evaluate the efficacy of prospective random undersampling and low-dimensional-structure self-learning and thresholding reconstruction for highly accelerated contrast-enhanced whole-heart coronary MRI. A prospective random undersampling scheme was implemented using phase ordering to minimize artifacts due to gradient switching and was compared to a randomly undersampled acquisition with no profile ordering. This profile-ordering technique was then used to acquire contrast-enhanced whole-heart coronary MRI in 10 healthy subjects with 4-fold acceleration. Reconstructed images and the acquired zero-filled images were compared for depicted vessel length, vessel sharpness, and subjective image quality on a scale of 1 (poor) to 4 (excellent). In a pilot study, contrast-enhanced whole-heart coronary MRI was also acquired in four patients with suspected coronary artery disease with 3-fold acceleration. The undersampled images were reconstructed using low-dimensional-structure self-learning and thresholding, which showed significant improvement over the zero-filled images in both objective and subjective measures, with an overall score of 3.6 ± 0.5. Reconstructed images in patients were all diagnostic. Low-dimensional-structure self-learning and thresholding reconstruction allows contrast-enhanced whole-heart coronary MRI with acceleration as high as 4-fold using clinically available five-channel phased-array coil.

Rapid pediatric cardiac assessment of flow and ventricular volume with compressed sensing parallel imaging volumetric cine phase-contrast MRI

OBJECTIVE

The quantification of cardiac flow and ventricular volumes is an essential goal of many congenital heart MRI examinations, often requiring acquisition of multiple 2D phase-contrast and bright-blood cine steady-state free precession (SSFP) planes. Scan acquisition, however, is lengthy and highly reliant on an imager who is well-versed in structural heart disease. Although it can also be lengthy, 3D time-resolved (4D) phase-contrast MRI yields global flow patterns and is simpler to perform. We therefore sought to accelerate 4D phase contrast and to determine whether equivalent flow and volume measurements could be extracted.

MATERIALS AND METHODS

Four-dimensional phase contrast was modified for higher acceleration with compressed sensing. Custom software was developed to process 4D phase-contrast images. We studied 29 patients referred for congenital cardiac MRI who underwent a routine clinical protocol, including cine short-axis stack SSFP and 2D phase contrast, followed by contrast-enhanced 4D phase contrast. To compare quantitative measurements, Bland-Altman analysis, paired Student t tests, and F tests were used.

RESULTS

Ventricular end-diastolic, end-systolic, and stroke volumes obtained from 4D phase contrast and SSFP were well correlated (ρ = 0.91-0.95; r(2) = 0.83-0.90), with no statistically significant difference. Ejection fractions were well correlated in a subpopulation that underwent higher-resolution compressed-sensing 4D phase contrast (ρ = 0.88; r(2) = 0.77). Four-dimensional phase contrast and 2D phase contrast flow rates were also well correlated (ρ = 0.90; r(2) = 0.82). Excluding ventricles with valvular insufficiency, cardiac outputs derived from outlet valve flow and stroke volumes were more consistent by 4D phase contrast than by 2D phase contrast and SSFP.

CONCLUSION

Combined parallel imaging and compressed sensing can be applied to 4D phase contrast. With custom software, flow and ventricular volumes may be extracted with comparable accuracy to SSFP and 2D phase contrast. Furthermore, cardiac outputs were more consistent by 4D phase contrast.

Coil compression for accelerated imaging with Cartesian sampling

MRI using receiver arrays with many coil elements can provide high signal-to-noise ratio and increase parallel imaging acceleration. At the same time, the growing number of elements results in larger datasets and more computation in the reconstruction. This is of particular concern in 3D acquisitions and in iterative reconstructions. Coil compression algorithms are effective in mitigating this problem by compressing data from many channels into fewer virtual coils. In Cartesian sampling there often are fully sampled k-space dimensions. In this work, a new coil compression technique for Cartesian sampling is presented that exploits the spatially varying coil sensitivities in these nonsubsampled dimensions for better compression and computation reduction. Instead of directly compressing in k-space, coil compression is performed separately for each spatial location along the fully sampled directions, followed by an additional alignment process that guarantees the smoothness of the virtual coil sensitivities. This important step provides compatibility with autocalibrating parallel imaging techniques. Its performance is not susceptible to artifacts caused by a tight imaging field-of-view. High quality compression of in vivo 3D data from a 32 channel pediatric coil into six virtual coils is demonstrated.

Inverse field-based approach for simultaneous B₁ mapping at high fields - a phantom based study

Based on computational electromagnetics and multi-level optimization, an inverse approach of attaining accurate mapping of both transmit and receive sensitivity of radiofrequency coils is presented. This paper extends our previous study of inverse methods of receptivity mapping at low fields, to allow accurate mapping of RF magnetic fields (B(1)) for high-field applications. Accurate receive sensitivity mapping is essential to image domain parallel imaging methods, such as sensitivity encoding (SENSE), to reconstruct high quality images. Accurate transmit sensitivity mapping will facilitate RF-shimming and parallel transmission techniques that directly address the RF inhomogeneity issue, arguably the most challenging issue of high-field magnetic resonance imaging (MRI). The inverse field-based approach proposed herein is based on computational electromagnetics and iterative optimization. It fits an experimental image to the numerically calculated signal intensity by iteratively optimizing the coil-subject geometry to better resemble the experiments. Accurate transmit and receive sensitivities are derived as intermediate results of the optimization process. The method is validated by imaging studies using homogeneous saline phantom at 7T. A simulation study at 300MHz demonstrates that the proposed method is able to obtain receptivity mapping with errors an order of magnitude less than that of the conventional method. The more accurate receptivity mapping and simultaneously obtained transmit sensitivity mapping could enable artefact-reduced and intensity-corrected image reconstructions. It is hoped that by providing an approach to the accurate mapping of both transmit and receive sensitivity, the proposed method will facilitate a range of applications in high-field MRI and parallel imaging.

Spread spectrum magnetic resonance imaging

We propose a novel compressed sensing technique to accelerate the magnetic resonance imaging (MRI) acquisition process. The method, coined spread spectrum MRI or simply s(2)MRI, consists of premodulating the signal of interest by a linear chirp before random k-space under-sampling, and then reconstructing the signal with nonlinear algorithms that promote sparsity. The effectiveness of the procedure is theoretically underpinned by the optimization of the coherence between the sparsity and sensing bases. The proposed technique is thoroughly studied by means of numerical simulations, as well as phantom and in vivo experiments on a 7T scanner. Our results suggest that s(2)MRI performs better than state-of-the-art variable density k-space under-sampling approaches.

Parallel imaging with nonlinear reconstruction using variational penalties

A new approach based on nonlinear inversion for autocalibrated parallel imaging with arbitrary sampling patterns is presented. By extending the iteratively regularized Gauss-Newton method with variational penalties, the improved reconstruction quality obtained from joint estimation of image and coil sensitivities is combined with the superior noise suppression of total variation and total generalized variation regularization. In addition, the proposed approach can lead to enhanced removal of sampling artifacts arising from pseudorandom and radial sampling patterns. This is demonstrated for phantom and in vivo measurements.

Denoising sparse images from GRAPPA using the nullspace method

To accelerate magnetic resonance imaging using uniformly undersampled (nonrandom) parallel imaging beyond what is achievable with generalized autocalibrating partially parallel acquisitions (GRAPPA) alone, the DEnoising of Sparse Images from GRAPPA using the Nullspace method is developed. The trade-off between denoising and smoothing the GRAPPA solution is studied for different levels of acceleration. Several brain images reconstructed from uniformly undersampled k-space data using DEnoising of Sparse Images from GRAPPA using the Nullspace method are compared against reconstructions using existing methods in terms of difference images (a qualitative measure), peak-signal-to-noise ratio, and noise amplification (g-factors) as measured using the pseudo-multiple replica method. Effects of smoothing, including contrast loss, are studied in synthetic phantom data. In the experiments presented, the contrast loss and spatial resolution are competitive with existing methods. Results for several brain images demonstrate significant improvements over GRAPPA at high acceleration factors in denoising performance with limited blurring or smoothing artifacts. In addition, the measured g-factors suggest that DEnoising of Sparse Images from GRAPPA using the Nullspace method mitigates noise amplification better than both GRAPPA and L1 iterative self-consistent parallel imaging reconstruction (the latter limited here by uniform undersampling).

Fast undersampled functional magnetic resonance imaging using nonlinear regularized parallel image reconstruction

In this article we aim at improving the performance of whole brain functional imaging at very high temporal resolution (100 ms or less). This is achieved by utilizing a nonlinear regularized parallel image reconstruction scheme, where the penalty term of the cost function is set to the L(1)-norm measured in some transform domain. This type of image reconstruction has gained much attention recently due to its application in compressed sensing and has proven to yield superior spatial resolution and image quality over e.g. Tikhonov regularized image reconstruction. We demonstrate that by using nonlinear regularization it is possible to more accurately localize brain activation from highly undersampled k-space data at the expense of an increase in computation time.

K-t sparse GROWL: sequential combination of partially parallel imaging and compressed sensing in k-t space using flexible virtual coil

Because dynamic MR images are often sparse in x-f domain, k-t space compressed sensing (k-t CS) has been proposed for highly accelerated dynamic MRI. When a multichannel coil is used for acquisition, the combination of partially parallel imaging and k-t CS can improve the accuracy of reconstruction. In this work, an efficient combination method is presented, which is called k-t sparse Generalized GRAPPA fOr Wider readout Line. One fundamental aspect of this work is to apply partially parallel imaging and k-t CS sequentially. A partially parallel imaging technique using a Generalized GRAPPA fOr Wider readout Line operator is adopted before k-t CS reconstruction to decrease the reduction factor in a computationally efficient way while preserving temporal resolution. Channel combination and relative sensitivity maps are used in the flexible virtual coil scheme to alleviate the k-t CS computational load with increasing number of channels. Using k-t FOCUSS as a specific example of k-t CS, the experiments with Cartesian and radial data sets demonstrate that k-t sparse Generalized GRAPPA fOr Wider readout Line can produce results with two times lower root-mean-square error than conventional channel-by-channel k-t CS while consuming up to seven times less computational cost.

Compressed-sensing motion compensation (CosMo): a joint prospective-retrospective respiratory navigator for coronary MRI

Prospective right hemidiaphragm navigator (NAV) is commonly used in free-breathing coronary MRI. The NAV results in an increase in acquisition time to allow for resampling of the motion-corrupted k-space data. In this study, we are presenting a joint prospective-retrospective NAV motion compensation algorithm called compressed-sensing motion compensation (CosMo). The inner k-space region is acquired using a prospective NAV; for the outer k-space, a NAV is only used to reject the motion-corrupted data without reacquiring them. Subsequently, those unfilled k-space lines are retrospectively estimated using compressed sensing reconstruction. We imaged right coronary artery in nine healthy adult subjects. An undersampling probability map and sidelobe-to-peak ratio were calculated to study the pattern of undersampling, generated by NAV. Right coronary artery images were then retrospectively reconstructed using compressed-sensing motion compensation for gating windows between 3 and 10 mm and compared with the ones fully acquired within the gating windows. Qualitative imaging score and quantitative vessel sharpness were calculated for each reconstruction. The probability map and sidelobe-to-peak ratio show that the NAV generates a random undersampling k-space pattern. There were no statistically significant differences between the vessel sharpness and subjective score of the two reconstructions. Compressed-sensing motion compensation could be an alternative motion compensation technique for free-breathing coronary MRI that can be used to reduce scan time.

High-Performance 3D Compressive Sensing MRI Reconstruction Using Many-Core Architectures

Compressive sensing (CS) describes how sparse signals can be accurately reconstructed from many fewer samples than required by the Nyquist criterion. Since MRI scan duration is proportional to the number of acquired samples, CS has been gaining significant attention in MRI. However, the computationally intensive nature of CS reconstructions has precluded their use in routine clinical practice. In this work, we investigate how different throughput-oriented architectures can benefit one CS algorithm and what levels of acceleration are feasible on different modern platforms. We demonstrate that a CUDA-based code running on an NVIDIA Tesla C2050 GPU can reconstruct a 256 × 160 × 80 volume from an 8-channel acquisition in 19 seconds, which is in itself a significant improvement over the state of the art. We then show that Intel's Knights Ferry can perform the same 3D MRI reconstruction in only 12 seconds, bringing CS methods even closer to clinical viability.

Improved least squares MR image reconstruction using estimates of k-space data consistency

This study describes a new approach to reconstruct data that has been corrupted by unfavorable magnetization evolution. In this new framework, images are reconstructed in a weighted least squares fashion using all available data and a measure of consistency determined from the data itself. The reconstruction scheme optimally balances uncertainties from noise error with those from data inconsistency, is compatible with methods that model signal corruption, and may be advantageous for more accurate and precise reconstruction with many least squares-based image estimation techniques including parallel imaging and constrained reconstruction/compressed sensing applications. Performance of the several variants of the algorithm tailored for fast spin echo and self-gated respiratory gating applications was evaluated in simulations, phantom experiments, and in vivo scans. The data consistency weighting technique substantially improved image quality and reduced noise as compared to traditional reconstruction approaches.

Parallel magnetic resonance imaging using localized receive arrays with sinc interpolation (PILARS)

Large arrays with localized coil sensitivity make it possible to use parallel imaging to significantly accelerate MR imaging speed. However, the need for auto calibration signals limits the actual acceleration factors achievable with large arrays. This paper presents a novel method for parallel imaging with large arrays. The method uses Sinc kernels for k-space data interpolation that only requires one phase parameter to be estimated using a small size of calibration signals. Simulations based on synthetic array data and phantom experiments show that the new method can achieve higher actual acceleration factors with comparable reconstruction quality.

Resonant Mode Reduction in Radiofrequency Volume Coils for Ultrahigh Field Magnetic Resonance Imaging

In a multimodal volume coil, only one mode can generate homogeneous Radiofrequency (RF) field for Magnetic Resonance Imaging. The existence of other modes may increase the volume coil design difficulties and potentially decreases coil performance. In this study, we introduce common-mode resonator technique to high and ultrahigh field volume coil designs to reduce the resonant mode while maintain the homogeneity of the RF field. To investigate the design method, the common-mode resonator was realized by using a microstrip line which was split along the central to become a pair of parallel transmission lines within which common-mode currents exist. Eight common-mode resonators were placed equidistantly along the circumference of a low loss dielectric cylinder to form a volume coil. Theoretical analysis and comparison between the 16-strut common-mode volume coil and a conventional 16-strut volume coil in terms of RF field homogeneity and efficiency was performed using Finite-Difference Time-Domain (FDTD) method at 298.2 MHz. MR imaging experiments were performed by using a prototype of the common-mode volume coil on a whole body 7 Tesla scanner. FDTD simulation results showed the reduced number of resonant modes of the common-mode volume coil over the conventional volume coil, while the RF field homogeneity of the two type volume coils was kept at the same level. MR imaging of a water phantom and a kiwi fruit showing the feasibility of the proposed method for simplifying the volume coil design is also presented.

Computational acceleration for MR image reconstruction in partially parallel imaging

In this paper, we present a fast numerical algorithm for solving total variation and l(1) (TVL1) based image reconstruction with application in partially parallel magnetic resonance imaging. Our algorithm uses variable splitting method to reduce computational cost. Moreover, the Barzilai-Borwein step size selection method is adopted in our algorithm for much faster convergence. Experimental results on clinical partially parallel imaging data demonstrate that the proposed algorithm requires much fewer iterations and/or less computational cost than recently developed operator splitting and Bregman operator splitting methods, which can deal with a general sensing matrix in reconstruction framework, to get similar or even better quality of reconstructed images.

Low-dimensional-structure self-learning and thresholding: regularization beyond compressed sensing for MRI reconstruction

An improved image reconstruction method from undersampled k-space data, low-dimensional-structure self-learning and thresholding (LOST), which utilizes the structure from the underlying image is presented. A low-resolution image from the fully sampled k-space center is reconstructed to learn image patches of similar anatomical characteristics. These patches are arranged into "similarity clusters," which are subsequently processed for dealiasing and artifact removal, using underlying low-dimensional properties. The efficacy of the proposed method in scan time reduction was assessed in a pilot coronary MRI study. Initially, in a retrospective study on 10 healthy adult subjects, we evaluated retrospective undersampling and reconstruction using LOST, wavelet-based l(1)-norm minimization, and total variation compressed sensing. Quantitative measures of vessel sharpness and mean square error, and qualitative image scores were used to compare reconstruction for rates of 2, 3, and 4. Subsequently, in a prospective study, coronary MRI data were acquired using these rates, and LOST-reconstructed images were compared with an accelerated data acquisition using uniform undersampling and sensitivity encoding reconstruction. Subjective image quality and sharpness data indicate that LOST outperforms the alternative techniques for all rates. The prospective LOST yields images with superior quality compared with sensitivity encoding or l(1)-minimization compressed sensing. The proposed LOST technique greatly improves image reconstruction for accelerated coronary MRI acquisitions.

Fast concomitant gradient field and field inhomogeneity correction for spiral cardiac imaging

Non-Cartesian imaging provides many advantages in terms of flexibility, functionality, and speed. However, a major drawback to these imaging methods is off-resonance distortion artifacts. These artifacts manifest as blurring in spiral imaging. Common techniques that remove the off-resonance field inhomogeneity distortion effects are not sufficient, because the high order concomitant gradient fields are nontrivial for common imaging conditions, such as imaging 5 cm off isocenter in an 1.5 T scanner. Previous correction algorithms are either slow or do not take into account the known effects of concomitant gradient fields along with the field inhomogeneities. To ease the correction, the distortion effects are modeled as a non-stationary convolution problem. In this work, two fast and accurate postgridding algorithms are presented and analyzed. These methods account for both the concomitant field effects and the field inhomogeneities. One algorithm operates in the frequency domain and the other in the spatial domain. To take advantage of their speed and accuracy, the algorithms are applied to a real-time cardiac study and a high-resolution cardiac study. Both of the presented algorithms provide for a practical solution to the off-resonance problem in spiral imaging.

PRACTICAL PARALLEL IMAGING COMPRESSED SENSING MRI: SUMMARY OF TWO YEARS OF EXPERIENCE IN ACCELERATING BODY MRI OF PEDIATRIC PATIENTS

For the last two years, we have been experimenting with applying compressed sensing parallel imaging for body imaging of pediatric patients. It is a joint-effort by teams from UC Berkeley, Stanford University and GE Healthcare. This paper aims to summarize our experience so far. We describe our acquisition approach: 3D spoiled-gradient-echo with poisson-disc random undersampling of the phase encodes. Our re-construction approach: ℓ₁-SPIRiT, an iterative autocalibrating parallel imaging reconstruction that enforces both data consistency and joint-sparsity in the wavelet domain. Our implementation: an on-line parallelized implementation of ℓ₁-SPIRiT on multi-core CPU and General Purpose Graphics Processors (GPGPU) that achieves sub-minute 3D reconstructions with 8-channels. Clinical results showing higher quality reconstruction and better diagnostic confidence than parallel imaging alone at accelerations on the order of number of coils.

Adapted random sampling patterns for accelerated MRI

OBJECTIVE

Variable density random sampling patterns have recently become increasingly popular for accelerated imaging strategies, as they lead to incoherent aliasing artifacts. However, the design of these sampling patterns is still an open problem. Current strategies use model assumptions like polynomials of different order to generate a probability density function that is then used to generate the sampling pattern. This approach relies on the optimization of design parameters which is very time consuming and therefore impractical for daily clinical use.

MATERIALS AND METHODS

This work presents a new approach that generates sampling patterns by making use of power spectra of existing reference data sets and hence requires neither parameter tuning nor an a priori mathematical model of the density of sampling points.

RESULTS

The approach is validated with downsampling experiments, as well as with accelerated in vivo measurements. The proposed approach is compared with established sampling patterns, and the generalization potential is tested by using a range of reference images. Quantitative evaluation is performed for the downsampling experiments using RMS differences to the original, fully sampled data set.

CONCLUSION

Our results demonstrate that the image quality of the method presented in this paper is comparable to that of an established model-based strategy when optimization of the model parameter is carried out and yields superior results to non-optimized model parameters. However, no random sampling pattern showed superior performance when compared to conventional Cartesian subsampling for the considered reconstruction strategy.

Rapid flow quantification in iliac arteries with spiral phase-contrast MRI

Phase contrast MRI is a powerful tool for blood flow quantification. Conventional cartesian phase contrast sequences require lengthy acquisition on the order of several minutes. Spiral acquisition phase-contrast (PC) MRI is capable of reducing the TR and TE in order to minimize flow dependent artifacts and total imaging time. Despite this, in general, spiral phase contrast sequences suffer from off-resonance artifacts and inconsistent data artifacts. In this work, we show that short interleaved spiral readout trajectories have the capability to obtain high spatio-temporal resolution flow images in the common iliac artery distal to the aortoiliac bifurcation with little or no artifacts and with significant savings in image acquisition time over the Cartesian trajectory. To verify the accuracy, we compare our results with a Conventional cartesian trajectory.

Novel 16-channel receive coil array for accelerated upper airway MRI at 3 Tesla

Upper airway MRI can provide a noninvasive assessment of speech and swallowing disorders and sleep apnea. Recent work has demonstrated the value of high-resolution three-dimensional imaging and dynamic two-dimensional imaging and the importance of further improvements in spatio-temporal resolution. The purpose of the study was to describe a novel 16-channel 3 Tesla receive coil that is highly sensitive to the human upper airway and investigate the performance of accelerated upper airway MRI with the coil. In three-dimensional imaging of the upper airway during static posture, 6-fold acceleration is demonstrated using parallel imaging, potentially leading to capturing a whole three-dimensional vocal tract with 1.25 mm isotropic resolution within 9 sec of sustained sound production. Midsagittal spiral parallel imaging of vocal tract dynamics during natural speech production is demonstrated with 2 × 2 mm(2) in-plane spatial and 84 ms temporal resolution.

Improved pediatric MR imaging with compressed sensing

PURPOSE

To develop a method that combines parallel imaging and compressed sensing to enable faster and/or higher spatial resolution magnetic resonance (MR) imaging and show its feasibility in a pediatric clinical setting.

MATERIALS AND METHODS

Institutional review board approval was obtained for this HIPAA-compliant study, and informed consent or assent was given by subjects. A pseudorandom k-space undersampling pattern was incorporated into a three-dimensional (3D) gradient-echo sequence; aliasing then has an incoherent noiselike pattern rather than the usual coherent fold-over wrapping pattern. This k-space-sampling pattern was combined with a compressed sensing nonlinear reconstruction method that exploits the assumption of sparsity of medical images to permit reconstruction from undersampled k-space data and remove the noiselike aliasing. Thirty-four patients (15 female and 19 male patients; mean age, 8.1 years; range, 0-17 years) referred for cardiovascular, abdominal, and knee MR imaging were scanned with this 3D gradient-echo sequence at high acceleration factors. Obtained k-space data were reconstructed with both a traditional parallel imaging algorithm and the nonlinear method. Both sets of images were rated for image quality, radiologist preference, and delineation of specific structures by two radiologists. Wilcoxon and symmetry tests were performed to test the hypothesis that there was no significant difference in ratings for image quality, preference, and delineation of specific structures.

RESULTS

Compressed sensing images were preferred more often, had significantly higher image quality ratings, and greater delineation of anatomic structures (P < .001) than did images obtained with the traditional parallel reconstruction method.

CONCLUSION

A combination of parallel imaging and compressed sensing is feasible in a clinical setting and may provide higher resolution and/or faster imaging, addressing the challenge of delineating anatomic structures in pediatric MR imaging.