Partial fourier partially parallel imaging

Use of Compressed Sensing Accelerated, Low-Velocity Encoded, Isotropic Resolution, Phase Contrast Magnetic Resonance Angiography for SEEG Electrode Implantation

OBJECTIVE

We assessed the feasibility of using compressed sensing accelerated, low-velocity encoded, isotropic resolution phase contrast (CLIP) magnetic resonance angiography (MRA) for avascular trajectory planning of stereoelectroencephalography.

METHODS

Ten healthy subjects (1 woman and 9 men; age, 33.6 ± 9.0 years) and 20 consecutive patients (12 female patients; age, 22 ± 13.6 years) were enrolled in the present study. The healthy subjects underwent CLIP-MRA, and 3 other phase contrast MRA protocols with conventional parallel imaging (PI) acceleration, including low resolution with twofold PI (PI2), high resolution (HR) with fivefold PI (PI5), and HR-PI2. The patients underwent CLIP-MRA and computed tomography angiography (CTA). The image qualities were evaluated. The numbers and locations of trajectory-vessel conflict detected using CLIP-MRA were noted.

RESULTS

With similar scan durations, CLIP-MRA achieved higher spatial resolution compared with low resolution with PI2 and detected significantly more branches compared with HR-PI5. With the same spatial resolution, the signal/noise and contrast/noise ratios of CLIP-MRA were higher than those with HR-PI2 with a shorter scan duration. For the 12 adult patients (10 female patients; 28.8 ± 12.7 years), CLIP-MRA had better signal/noise and contrast/noise ratios than CTA. The trajectory had required modification for 14 of the 20 patients (70%), with a proportion of trajectory modification of 10.7% (23 of 215 electrodes). The middle meningeal artery, cortical vessel, and skull vessel were the main vessels with conflict (n = 11, n = 7, and n = 5, respectively).

CONCLUSIONS

In the present study, CLIP-MRA provided a clear cortical vascular display noninvasively without intravascular contrast and radiation. The middle meningeal artery and diploic and emissary veins were the main conflict vessels and could be clearly displayed using CLIP-MRA but not CTA.

On Ambiguity in Linear Inverse Problems: Entrywise Bounds on Nearly Data-Consistent Solutions and Entrywise Condition Numbers

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree of ambiguity that may exist about its solution. Traditional measures of ill-posedness, such as the condition number of a matrix, provide characterizations that are global in nature. While such characterizations can be powerful, they can also fail to provide full insight into situations where certain entries of the solution vector are more or less ambiguous than others. In this work, we derive novel theoretical lower- and upper-bounds that apply to individual entries of the solution vector, and are valid for all potential solution vectors that are nearly data-consistent. These bounds are agnostic to the noise statistics and the specific method used to solve the inverse problem, and are also shown to be tight. In addition, our results also lead us to introduce an entrywise version of the traditional condition number, which provides a substantially more nuanced characterization of scenarios where certain elements of the solution vector are less sensitive to perturbations than others. Our results are illustrated in an application to magnetic resonance imaging reconstruction, and we include discussions of practical computation methods for large-scale inverse problems, connections between our new theory and the traditional Cramér-Rao bound under statistical modeling assumptions, and potential extensions to cases involving constraints beyond just data-consistency.

Efficient iterative solutions to complex-valued nonlinear least-squares problems with mixed linear and antilinear operators

We consider a setting in which it is desired to find an optimal complex vector x ∈ C ^N that satisfies A (x) ≈ b in a least-squares sense, where b ∈ C ^M is a data vector (possibly noise-corrupted), and A (·) : C ^N → C ^M is a measurement operator. If A (·) were linear, this reduces to the classical linear least-squares problem, which has a well-known analytic solution as well as powerful iterative solution algorithms. However, instead of linear least-squares, this work considers the more complicated scenario where A (·) is nonlinear, but can be represented as the summation and/or composition of some operators that are linear and some operators that are antilinear. Some common nonlinear operations that have this structure include complex conjugation or taking the real-part or imaginary-part of a complex vector. Previous literature has shown that this kind of mixed linear/antilinear least-squares problem can be mapped into a linear least-squares problem by considering x as a vector in R ^2N instead of C ^N . While this approach is valid, the replacement of the original complex-valued optimization problem with a real-valued optimization problem can be complicated to implement, and can also be associated with increased computational complexity. In this work, we describe theory and computational methods that enable mixed linear/antilinear least-squares problems to be solved iteratively using standard linear least-squares tools, while retaining all of the complex-valued structure of the original inverse problem. An illustration is providedtodemonstratethatthisapproachcansimplifytheimplementationandreduce the computational complexity of iterative solution algorithms.

Local perturbation responses and checkerboard tests: Characterization tools for nonlinear MRI methods

PURPOSE

Modern methods for MR image reconstruction, denoising, and parameter mapping are becoming increasingly nonlinear, black-box, and at risk of "hallucination." These trends mean that traditional tools for judging confidence in an image (visual quality assessment, point-spread functions (PSFs), g-factor maps, etc.) are less helpful than before. This paper describes and evaluates an approach that can help with assessing confidence in images produced by arbitrary nonlinear methods.

THEORY AND METHODS

We propose to characterize nonlinear methods by examining the images they produce before and after applying controlled perturbations to the measured data. This results in functions known as local perturbation responses (LPRs) that can provide useful insight into sensitivity, spatial resolution, and aliasing characteristics. LPRs can be viewed as generalizations of classical PSFs, and are are very flexible-they can be applied to arbitary nonlinear methods and arbitrary datasets across a range of different reconstruction, denoising, and parameter mapping applications. Importantly, LPRs do not require a ground truth image.

RESULTS

Impulse-based and checkerboard-pattern LPRs are demonstrated in image reconstruction and denoising scenarios. We observe that these LPRs provide insights into spatial resolution, signal leakage, and aliasing that are not available with other methods. We also observe that popular reference-based image quality metrics (eg, mean-squared error and structural similarity) do not always correlate with good LPR characteristics.

CONCLUSIONS

LPRs are a useful tool that can be used to characterize and assess confidence in nonlinear MR methods, and provide insights that are distinct from and complementary to existing quality assessments.

On the signal-to-noise ratio benefit of spiral acquisition in diffusion MRI

PURPOSE

Spiral readouts combine several favorable properties that promise superior net sensitivity for diffusion imaging. The purpose of this study is to verify the signal-to-noise ratio (SNR) benefit of spiral acquisition in comparison with current echo-planar imaging (EPI) schemes.

METHODS

Diffusion-weighted in vivo brain data from three subjects were acquired with a single-shot spiral sequence and several variants of single-shot EPI, including full-Fourier and partial-Fourier readouts as well as different diffusion-encoding schemes. Image reconstruction was based on an expanded signal model including field dynamics obtained by concurrent field monitoring. The effective resolution of each sequence was matched to that of full-Fourier EPI with 1 mm nominal resolution. SNR maps were generated by determining the noise statistics of the raw data and analyzing the propagation of equivalent synthetic noise through image reconstruction. Using the same approach, maps of noise amplification due to parallel imaging (g-factor) were calculated for different acceleration factors.

RESULTS

Relative to full-Fourier EPI at b = 0 s/mm² , spiral acquisition yielded SNR gains of 42-88% and 40-89% in white and gray matter, respectively, depending on the diffusion-encoding scheme. Relative to partial-Fourier EPI, the gains were 36-44% and 34-42%. Spiral g-factor maps exhibited less spatial variation and lower maxima than their EPI counterparts.

CONCLUSION

Spiral readouts achieve significant SNR gains in the order of 40-80% over EPI in diffusion imaging at 3T. Combining systematic effects of shorter echo time, readout efficiency, and favorable g-factor behavior, similar benefits are expected across clinical and neurosciences uses of diffusion imaging.

Full utilization of conjugate symmetry: combining virtual conjugate coil reconstruction with partial Fourier imaging for g-factor reduction in accelerated MRI

PURPOSE

In this study we propose a method to combine the parallel virtual conjugate coil (VCC) reconstruction with partial Fourier (PF) acquisition to improve reconstruction conditioning and reduce noise amplification in accelerated MRI where PF is used.

METHODS

Accelerated measurements are reconstructed in k-space by GRAPPA, with a VCC reconstruction kernel trained and applied in the central, symmetrically sampled part of k-space, while standard reconstruction is performed on the asymmetrically sampled periphery. The two reconstructed regions are merged to form a full reconstructed dataset, followed by PF reconstruction. The method is tested in vivo using T1-weighted spin-echo and T2*-weighted gradient-echo echo planar imaging (EPI) sequences, using both in-plane and simultaneous multislice (SMS) acceleration, at 1.5T and 3T field strengths. Noise amplification is estimated with theoretical calculations and pseudo-multiple-replica computations, for different PF factors, using zero-filling, homodyne, and projection onto convex sets (POCS) PF reconstruction.

RESULTS

Depending on the PF algorithm and the inherent benefit of VCC reconstruction without PF, approximately 35% to 80%, 15% to 60%, and 5% to 30% of that intrinsic SNR gain can be retained for PF factors 7/8, 6/8, and 5/8, respectively, by including the VCC signals in the reconstruction. Compared with VCC-reconstructed acquisitions of higher acceleration, without PF, but having the same net acceleration, the combined method can provide a higher SNR if the inherent benefit of VCC is low or moderate.

CONCLUSION

The proposed technique enables the partial application of VCC reconstruction to measurements with PF using either in-plane or SMS acceleration, and therefore can reduce the noise amplification of such acquisitions.

On the limitations of partial Fourier acquisition in phase-contrast MRI of turbulent kinetic energy

PURPOSE

To investigate limitations of partial Fourier acquisition in phase-contrast MRI of turbulent kinetic energy (TKE).

METHODS

To assess the validity of partial Fourier reconstruction of TKE and phase images, computational fluid dynamics data of mean and turbulent velocities in a stenotic U-bend phantom was used. Partial Fourier acquisition with 75% k-space coverage was simulated and TKE data were reconstructed using zero-filling, homodyne reconstruction, and the method of projections onto convex sets (POCS). Results were compared to data from fully sampled k-space and 75% symmetric sampling. In addition, compressed sensing (CS) reconstruction was compared for a standard variable density sampling pattern and a variable density sampling pattern combined with 75% partial Fourier. For illustration purposes, in vivo examples of velocity magnitude and TKE maps of aortic flow reconstructed with the different methods are provided.

RESULTS

In accordance with theory, partial Fourier reconstruction of TKE maps from phase-contrast data results in artifacts relative to fully sampled data. It is demonstrated that neither homodyne reconstruction nor POCS can improve reconstruction of TKE data with respect to zero-filling reconstruction when compared to ground-truth (RMS error: 4.70%, 4.34%, and 2.45% for homodyne, POCS, and zero-filling reconstruction of in vivo data, respectively). CS reconstruction from data acquired with partial Fourier did not recover the resolution loss incurred by partial Fourier sampling.

CONCLUSION

Partial Fourier reconstruction of TKE maps from phase-contrast data does not yield a benefit over zero-filling reconstruction. In consequence, symmetric sampling is preferred over partial Fourier acquisition for a given number of phase-encodes in phase-contrast MRI.

Hybrid PET/MRI Methodology

The hybrid PET/MR scanner represents the first implementation of the effective integration of two modalities allowing truly synchronous/simultaneous acquisition of their imaging signals. This integration, resulting from the innovation and development of specific hardware components has paved the way for new approaches in the study of neurodegenerative diseases. This chapter will describe the hardware development that has led to the availability of different clinical solutions for PET/MR imaging as well as the still-open technological challenges and opportunities related to the processing and exploitation of the simultaneous acquisition in neurological studies.

General phase regularized reconstruction using phase cycling

PURPOSE

To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging.

THEORY AND METHODS

The problem of enforcing phase constraints in reconstruction was studied under a regularized inverse problem framework. A general phase regularized reconstruction algorithm was proposed to enable various joint reconstruction of partial Fourier imaging, water-fat imaging and flow imaging, along with parallel imaging (PI) and compressed sensing (CS). Since phase regularized reconstruction is inherently non-convex and sensitive to phase wraps in the initial solution, a reconstruction technique, named phase cycling, was proposed to render the overall algorithm invariant to phase wraps. The proposed method was applied to retrospectively under-sampled in vivo datasets and compared with state of the art reconstruction methods.

RESULTS

Phase cycling reconstructions showed reduction of artifacts compared to reconstructions without phase cycling and achieved similar performances as state of the art results in partial Fourier, water-fat and divergence-free regularized flow reconstruction. Joint reconstruction of partial Fourier + water-fat imaging + PI + CS, and partial Fourier + divergence-free regularized flow imaging + PI + CS were demonstrated.

CONCLUSION

The proposed phase cycling reconstruction provides an alternative way to perform phase regularized reconstruction, without the need to perform phase unwrapping. It is robust to the choice of initial solutions and encourages the joint reconstruction of phase imaging applications. Magn Reson Med 80:112-125, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Characterizing and eliminating errors in enhancement and subtraction artifacts in dynamic contrast-enhanced breast MRI: Chemical shift artifact of the third kind

PURPOSE

To characterize errors in enhancement in breast dynamic contrast-enhanced (DCE) MRI studies as a function of echo time and determine the source of dark band artifacts in clinical subtraction images.

METHODS

Computer simulations, oil and water substitute (methylene chloride), as well as an American College of Radiology quality control phantom were tested. Routine clinical DCE breast MRI study was bracketed with (accelerated) in-phase DCE acquisitions in five patients.

RESULTS

Simulation results demonstrated up to -160% suppression of the expected enhancement caused by differential enhancement of fat and water. Two-dimensional gradient-recalled echo and fat-suppressed 3D GRE phantom imaging confirmed the simulation results and showed that fat suppression does not eliminate the artifact. In vivo in-phase DCE images showed increased enhancement consistent with predictions and also confirmed increased spatial blurring on in-phase 3D gradient-recalled echo images. Combined multi-dimensional partial Fourier and parallel imaging provided a time-equivalent in-phase DCE MRI acquisition.

CONCLUSION

Errors in expected enhancement occur in DCE breast MRI subtraction images because of differential enhancement of fat and water and incomplete fat signal suppression. These errors can lead to artificial suppression of enhancement as well as dark band artifacts on subtraction images. These artifacts can be eliminated with a time-equivalent in-phase fat-suppressed 3D gradient-recalled echo sequence. Understanding chemical shift artifact of the third kind, a unique artifact of artificial enhancement suppression in the presence of intravoxel fat and water signal, will aid DCE breast MRI image interpretation. In-phase acquisitions (combined with simultaneous minimum echo time or opposed-phase echoes) may facilitate qualitative, quantitative and longitudinal analysis of contrast enhancement. Magn Reson Med 79:2277-2289, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Fast Spatial Resolution Analysis of Quadratic Penalized Least-Squares Image Reconstruction With Separate Real and Imaginary Roughness Penalty: Application to fMRI

Penalized least-squares iterative image reconstruction algorithms used for spatial resolution-limited imaging, such as functional magnetic resonance imaging (fMRI), commonly use a quadratic roughness penalty to regularize the reconstructed images. When used for complex-valued images, the conventional roughness penalty regularizes the real and imaginary parts equally. However, these imaging methods sometimes benefit from separate penalties for each part. The spatial smoothness from the roughness penalty on the reconstructed image is dictated by the regularization parameter(s). One method to set the parameter to a desired smoothness level is to evaluate the full width at half maximum of the reconstruction method's local impulse response. Previous work has shown that when using the conventional quadratic roughness penalty, one can approximate the local impulse response using an FFT-based calculation. However, that acceleration method cannot be applied directly for separate real and imaginary regularization. This paper proposes a fast and stable calculation for this case that also uses FFT-based calculations to approximate the local impulse responses of the real and imaginary parts. This approach is demonstrated with a quadratic image reconstruction of fMRI data that uses separate roughness penalties for the real and imaginary parts.

Reducing sedation for pediatric body MRI using accelerated and abbreviated imaging protocols

Magnetic resonance imaging (MRI) is an established diagnostic imaging tool for investigating pediatric disease. MRI allows assessment of structure, function, and morphology in cardiovascular imaging, as well as tissue characterization in body imaging, without the use of ionizing radiation. For MRI in children, sedation and general anesthesia (GA) are often utilized to suppress patient motion, which can otherwise compromise image quality and diagnostic efficacy. However, evidence is emerging that use of sedation and GA in children might have long-term neurocognitive side effects, in addition to the short-term procedure-related risks. These concerns make risk-benefit assessment of sedation and GA more challenging. Therefore, reducing or eliminating the need for sedation and GA is an important goal of imaging innovation and research in pediatric MRI. In this review, the authors focus on technical and clinical approaches to reducing and eliminating the use of sedation in the pediatric population based on image acquisition acceleration and imaging protocols abbreviation. This paper covers important physiological and technical considerations for pediatric body MR imaging and discusses MRI techniques that offer the potential of recovering diagnostic-quality images from accelerated scans. In this review, the authors also introduce the concept of reporting elements for important indications for pediatric body MRI and use this as a basis for abbreviating the MR protocols. By employing appropriate accelerated and abbreviated approaches based on an understanding of the imaging needs and reporting elements for a given clinical indication, it is possible to reduce sedation and GA for pediatric chest, cardiovascular and abdominal MRI.

Recent advances in parallel imaging for MRI

Magnetic Resonance Imaging (MRI) is an essential technology in modern medicine. However, one of its main drawbacks is the long scan time needed to localize the MR signal in space to generate an image. This review article summarizes some basic principles and recent developments in parallel imaging, a class of image reconstruction techniques for shortening scan time. First, the fundamentals of MRI data acquisition are covered, including the concepts of k-space, undersampling, and aliasing. It is demonstrated that scan time can be reduced by sampling a smaller number of phase encoding lines in k-space; however, without further processing, the resulting images will be degraded by aliasing artifacts. Nearly all modern clinical scanners acquire data from multiple independent receiver coil arrays. Parallel imaging methods exploit properties of these coil arrays to separate aliased pixels in the image domain or to estimate missing k-space data using knowledge of nearby acquired k-space points. Three parallel imaging methods-SENSE, GRAPPA, and SPIRiT-are described in detail, since they are employed clinically and form the foundation for more advanced methods. These techniques can be extended to non-Cartesian sampling patterns, where the collected k-space points do not fall on a rectangular grid. Non-Cartesian acquisitions have several beneficial properties, the most important being the appearance of incoherent aliasing artifacts. Recent advances in simultaneous multi-slice imaging are presented next, which use parallel imaging to disentangle images of several slices that have been acquired at once. Parallel imaging can also be employed to accelerate 3D MRI, in which a contiguous volume is scanned rather than sequential slices. Another class of phase-constrained parallel imaging methods takes advantage of both image magnitude and phase to achieve better reconstruction performance. Finally, some applications are presented of parallel imaging being used to accelerate MR Spectroscopic Imaging.

Trimmed autocalibrating k-space estimation based on structured matrix completion

PURPOSE

Parallel imaging allows the reconstruction of undersampled data from multiple coils. This provides a means to reject and regenerate corrupt data (e.g. from motion artefact). The purpose of this work is to approach this problem using the SAKE parallel imaging method.

THEORY AND METHODS

Parallel imaging methods typically require calibration by fully sampling the center of k-space. This is a challenge in the presence of corrupted data, since the calibration data may be corrupted which leads to an errors-in-variables problem that cannot be solved by least squares or even iteratively reweighted least squares. The SAKE method, based on matrix completion and structured low rank approximation, was modified to detect and trim these errors from the data.

RESULTS

Simulated and actual corrupted datasets were reconstructed with SAKE, the proposed approach and a more standard reconstruction method (based on solving a linear equation) with a data rejection criterion. The proposed approach was found to reduce artefacts considerably in comparison to the other two methods.

CONCLUSION

SAKE with data trimming improves on previous methods for reconstructing images from grossly corrupted data.

Partial Discreteness: A Novel Prior for Magnetic Resonance Image Reconstruction

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

Real-based Polarity-preserving Asymmetric Fourier Imaging (RepAFI)

We proposed and assessed a modified asymmetric Fourier imaging (AFI) technique named real-based polarity-preserving AFI (RepAFI), in which the low-pass filter kernel for background phase estimation in AFI is optimized to preserve the magnetization polarity information for blood vessels and cerebrospinal fluid (CSF) even for data obtained using phase-sensitive inversion-recovery spin-echo-based (PSIR-SE) sequences with asymmetrical sampling in the k-space. Our proposed RepAFI technique achieves a practical balance of image quality and simplicity to provide better performance than conventional AFI methods.

Sparse Parallel MRI Based on Accelerated Operator Splitting Schemes

Recently, the sparsity which is implicit in MR images has been successfully exploited for fast MR imaging with incomplete acquisitions. In this paper, two novel algorithms are proposed to solve the sparse parallel MR imaging problem, which consists of l₁ regularization and fidelity terms. The two algorithms combine forward-backward operator splitting and Barzilai-Borwein schemes. Theoretically, the presented algorithms overcome the nondifferentiable property in l₁ regularization term. Meanwhile, they are able to treat a general matrix operator that may not be diagonalized by fast Fourier transform and to ensure that a well-conditioned optimization system of equations is simply solved. In addition, we build connections between the proposed algorithms and the state-of-the-art existing methods and prove their convergence with a constant stepsize in Appendix. Numerical results and comparisons with the advanced methods demonstrate the efficiency of proposed algorithms.

LORAKS makes better SENSE: Phase-constrained partial fourier SENSE reconstruction without phase calibration

PURPOSE

Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information.

THEORY AND METHODS

The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories.

RESULTS

Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches.

CONCLUSION

The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI. Magn Reson Med 77:1021-1035, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

High-spatial and high-temporal resolution dynamic contrast-enhanced perfusion imaging of the liver with time-resolved three-dimensional radial MRI

PURPOSE

Detection, characterization, and monitoring the treatment of hepatocellular carcinomas (HCC) in patients with cirrhosis is challenging because of their variable and rapid arterial enhancement. Multiphase dynamic contrast-enhanced MRI is used clinically for HCC assessment; however, the method suffers from limited temporal resolution and difficulty in coordinating imaging and breath-hold timing within a narrow temporal window of interest. In this article, a volumetric, high-spatial resolution, and high-temporal resolution dynamic contrast-enhanced liver imaging method for improved detection and characterization of HCC is demonstrated.

METHODS

A time-resolved three-dimensional radial acquisition with iterative sensitivity-encoding reconstruction images the entire abdomen and thorax with high spatial and temporal resolution, using real-time three-dimensional fluoroscopy to match the breath hold to contrast arrival. The sequence was tested on 17 subjects, including eight patients with HCC or other hypervascular focal lesions.

RESULTS

This technique was successful in acquiring volumetric imaging of the entire liver with 2.1-mm isotropic spatial and true 4-s temporal resolution.

CONCLUSION

This technique may be suitable for detecting, characterizing, and monitoring the treatment of HCC. It also holds significant potential for perfusion modeling, which may provide a noninvasive means to rapidly determine the efficacy of chemotherapeutic agents in these tumors over the entire liver volume.

Magnitude-based Asymmetric Fourier Imaging (MagAFI)

PURPOSE

We propose and assess 2 novel asymmetric Fourier imaging (AFI) techniques, magnitude-based AFI (MagAFI) and MagAFI combined with projection on to convex sets (POCS) (MagAFI+POCS). MagAFI does not require phase information because it uses only the magnitude image with zero-filling. MagAFI+POCS requires phase information but further reduces image errors.

MATERIALS AND METHODS

We initially compared phase maps obtained using asymmetrically sampled data for the whole of the k-space and symmetrically sampled data for the low frequency part of the k-space. We used one-dimensional simulation data and 3-dimensional gradient echo data for 2 different echo times (TEs) of the brains of volunteers and assessed the differences between the image reconstructed from the full k-space data and AFI images reconstructed from truncated k-space data. We generated AFI images in this study using the zero-filling, Margosian (homodyne), Margosian+POCS (standard POCS), MagAFI, and MagAFI+POCS techniques.

RESULTS

We confirmed the assumption of smaller phase errors for the full k-space data than for the symmetric low frequency k-space data. Our proposed MagAFI technique provides images with smaller phase-induced errors than those obtained using conventional methods, including standard POCS methods, which have been regarded as the best methods. MagAFI+POCS improves image quality as well as robustness.

CONCLUSION

Our proposed MagAFI technique achieves a practical balance of image quality and simplicity to perform better than conventional methods using only the 0-filled magnitude image. Combined with POCS, this technique can produce images of even better quality.

Three-dimensional echo planar imaging with controlled aliasing: A sequence for high temporal resolution functional MRI

PURPOSE

In this work, we combine three-dimensional echo planar imaging (3D-EPI) with controlled aliasing to substantially increase temporal resolution in whole-brain functional MRI (fMRI) while minimizing geometry-factor (g-factor) losses.

THEORY AND METHODS

The study was performed on a 7 Tesla scanner equipped with a 32-channel receive coil. The proposed 3D-EPI-CAIPI sequence was evaluated for: (i) image quality, compared with a conventionally undersampled parallel imaging acquisition; (ii) temporal resolution, the ability to sample and remove physiological signal fluctuations from the fMRI signal of interest and (iii) the ability to distinguish small changes in hemodynamic responses in an event-related fMRI experiment.

RESULTS

Whole-brain fMRI data with a voxel size of 2 × 2 × 2 mm(3) and temporal resolution of 371 ms could be acquired with acceptable image quality. Ten-fold parallel imaging accelerated 3D-EPI-CAIPI data were shown to lower the maximum g-factor losses up to 62% with respect to a 10-fold accelerated 3D-EPI dataset. FMRI with 400 ms temporal resolution allowed the detection of time-to-peak variations in functional responses due to multisensory facilitation in temporal, occipital and frontal cortices.

CONCLUSION

3D-EPI-CAIPI allows increased temporal resolution that enables better characterization of physiological noise, thus improving sensitivity to signal changes of interest. Furthermore, subtle changes in hemodynamic response dynamics can be studied in shorter scan times by avoiding the need for jittering. Magn Reson Med 75:2350-2361, 2016. © 2015 Wiley Periodicals, Inc.

Advances in real-time phase-contrast flow MRI using asymmetric radial gradient echoes

PURPOSE

To provide multidimensional velocity compensation for real-time phase-contrast flow MRI.

METHODS

The proposed method introduces asymmetric gradient echoes for highly undersampled radial FLASH MRI with phase-sensitive image reconstruction by regularized nonlinear inversion (NLINV). Using an adapted gradient delay correction the resulting image quality was analyzed by simulations and experimentally validated at 3 Tesla. For real-time flow MRI the reduced gradient-echo timing allowed for the incorporation of velocity-compensating waveforms for all imaging gradients at even shorter repetition times.

RESULTS

The results reveal a usable degree of 20% asymmetry. Real-time flow MRI with full velocity compensation eliminated signal void in a flow phantom, confirmed flow parameters in healthy subjects and demonstrated signal recovery and phase conservation in a patient with aortic valve insufficiency and stenosis. Exemplary protocols at 1.4-1.5 mm resolution and 6 mm slice thickness achieved total acquisition times of 33.3-35.7 ms for two images (7 spokes each) with and without flow-encoding gradient.

CONCLUSION

Asymmetric gradient echoes were successfully implemented for highly undersampled radial trajectories. The resulting temporal gain offers full velocity compensation for real-time phase-contrast flow MRI which minimizes false-positive contributions from complex flow and further enhances the temporal resolution compared with acquisitions with symmetric echoes.

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

PURPOSE

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

THEORY AND METHODS

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

RESULTS

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

CONCLUSION

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

Comparison of phase-constrained parallel MRI approaches: Analogies and differences

PURPOSE

Phase-constrained parallel MRI approaches have the potential for significantly improving the image quality of accelerated MRI scans. The purpose of this study was to investigate the properties of two different phase-constrained parallel MRI formulations, namely the standard phase-constrained approach and the virtual conjugate coil (VCC) concept utilizing conjugate k-space symmetry.

METHODS

Both formulations were combined with image-domain algorithms (SENSE) and a mathematical analysis was performed. Furthermore, the VCC concept was combined with k-space algorithms (GRAPPA and ESPIRiT) for image reconstruction. In vivo experiments were conducted to illustrate analogies and differences between the individual methods. Furthermore, a simple method of improving the signal-to-noise ratio by modifying the sampling scheme was implemented.

RESULTS

For SENSE, the VCC concept was mathematically equivalent to the standard phase-constrained formulation and therefore yielded identical results. In conjunction with k-space algorithms, the VCC concept provided more robust results when only a limited amount of calibration data were available. Additionally, VCC-GRAPPA reconstructed images provided spatial phase information with full resolution.

CONCLUSIONS

Although both phase-constrained parallel MRI formulations are very similar conceptually, there exist important differences between image-domain and k-space domain reconstructions regarding the calibration robustness and the availability of high-resolution phase information.

Noncontrast-enhanced peripheral venography using velocity-selective magnetization preparation and transient balanced SSFP

PURPOSE

To develop a three-dimensional (3D) noncontrast-enhanced (NCE) peripheral magnetic resonance venography (MRV) method and demonstrate its feasibility in vivo.

METHODS

The proposed MRV pulse sequence consisted of a velocity-selective (VS) inversion preparation module, inversion delay time (TI), fat inversion pulse, and 3D balanced steady-state free precession (bSSFP) dummy excitations and readout. The VS preparation module inverted arterial blood, which recovered close to zero magnetization during TI. The TI and the number of dummy excitations (Nnum ) were numerically optimized for maximizing vein-to-background contrast and tested in a healthy subject. The proposed MRV of the entire peripheral system, using four-station acquisition, was performed in six healthy subjects and three peripheral artery patients.

RESULTS

The numerical optimization yielded TI = 350 ms and Ndum  = 40, which was supported by the largest vein contrast among the parameters chosen around the optima on in vivo venograms. Four-station peripheral MRV using the optimized parameters well visualized all major deep veins with high vein-to-background contrast. The relative vein contrast ratios were 0.80 ± 0.08, 0.75 ± 0.07, and 0.84 ± 0.06 against the arteries, muscle, and fat, respectively.

CONCLUSION

The proposed NCE MRV using VS preparation and transient bSSFP can generate high-contrast peripheral venograms directly with a single acquisition.

An L1-norm phase constraint for half-Fourier compressed sensing in 3D MR imaging

OBJECTIVE

In most half-Fourier imaging methods, explicit phase replacement is used. In combination with parallel imaging, or compressed sensing, half-Fourier reconstruction is usually performed in a separate step. The purpose of this paper is to report that integration of half-Fourier reconstruction into iterative reconstruction minimizes reconstruction errors.

MATERIALS AND METHODS

The L1-norm phase constraint for half-Fourier imaging proposed in this work is compared with the L2-norm variant of the same algorithm, with several typical half-Fourier reconstruction methods. Half-Fourier imaging with the proposed phase constraint can be seamlessly combined with parallel imaging and compressed sensing to achieve high acceleration factors.

RESULTS

In simulations and in in-vivo experiments half-Fourier imaging with the proposed L1-norm phase constraint enables superior performance both reconstruction of image details and with regard to robustness against phase estimation errors.

CONCLUSION

The performance and feasibility of half-Fourier imaging with the proposed L1-norm phase constraint is reported. Its seamless combination with parallel imaging and compressed sensing enables use of greater acceleration in 3D MR imaging.

Regularization method for phase-constrained parallel MRI

PURPOSE

To implement a regularization method for the phase-constrained generalized partially parallel acquisitions (GRAPPA) algorithm to reduce image artifacts caused by data inconsistencies.

METHODS

Phase-constrained GRAPPA reconstructions are implemented through the use of virtual coils. To that end, synthetic virtual coils are generated by using complex conjugate symmetric signals from the actual coils. Regularization is achieved by applying coefficient-based penalty factors during the GRAPPA calibration procedure. Different penalizing factors are applied for the actual and virtual coils. The method is tested in vivo using T2-weighted turbo spin echo (TSE) images.

RESULTS

T2 signal decay perturbs conjugate k-space symmetry and produces artifacts in phase-constrained parallel MRI reconstructions of T2-weighted TSE images. Using the proposed regularization method, artifacts are suppressed at the cost of noise amplification. However, there is still a significant SNR gain compared with conventional GRAPPA.

CONCLUSION

The proposed regularization method is an efficient approach for artifact suppression and maintains the SNR benefit of phase-constrained parallel MRI over conventional parallel MRI.

Iterative k-t principal component analysis with nonrigid motion correction for dynamic three-dimensional cardiac perfusion imaging

PURPOSE

In this study, an iterative k-t principal component analysis (PCA) algorithm with nonrigid frame-to-frame motion correction is proposed for dynamic contrast-enhanced three-dimensional perfusion imaging.

METHODS

An iterative k-t PCA algorithm was implemented with regularization using training data corrected for frame-to-frame motion in the x-pc domain. Motion information was extracted using shape-constrained nonrigid image registration of the composite of training and k-t undersampled data. The approach was tested for 10-fold k-t undersampling using computer simulations and in vivo data sets corrupted by respiratory motion artifacts owing to free-breathing or interrupted breath-holds. Results were compared to breath-held reference data.

RESULTS

Motion-corrected k-t PCA image reconstruction resolved residual aliasing. Signal intensity curves extracted from the myocardium were close to those obtained from the breath-held reference. Upslopes were found to be more homogeneous in space when using the k-t PCA approach with motion correction.

CONCLUSIONS

Iterative k-t PCA with nonrigid motion correction permits correction of respiratory motion artifacts in three-dimensional first-pass myocardial perfusion imaging.

Multiband phase-constrained parallel MRI

PURPOSE

Parallel MRI methods are typically associated with a degradation of the signal-to-noise ratio (SNR). High scan time reduction factors are therefore restricted to applications with high intrinsic SNR. One possibility to increase the intrinsic SNR is to simultaneously excite several slices by means of multiband radio-frequency (RF) pulses and subsequently separate the slices by parallel MRI reconstruction algorithms. However, the separation of closely spaced slices may suffer from severe noise amplification when there is insufficient coil sensitivity variation along the slice direction. The purpose of this work is to apply a phase-constrained reconstruction for multiband experiments to minimize the noise amplification.

METHODS

Pre-defined phase differences between neighboring slices are induced and slice separation is performed by a phase-constrained parallel MRI reconstruction. Phase differences between neighboring slices are tailored to achieve optimal slice separation with minimized noise amplification. The potential of the method is demonstrated through multiband in-vivo experiments.

RESULTS

Noise amplification in multiband phase-constrained reconstructions is significantly reduced in comparison to standard multiband reconstruction when the phase difference between neighboring slices (distance = 12 mm) is 90°.

CONCLUSIONS

Multiband phase-constrained parallel MRI has the potential for accelerated multi-slice imaging with an improved SNR performance.

Improved diffusion imaging through SNR-enhancing joint reconstruction

Quantitative diffusion imaging is a powerful technique for the characterization of complex tissue microarchitecture. However, long acquisition times and limited signal-to-noise ratio represent significant hurdles for many in vivo applications. This article presents a new approach to reduce noise while largely maintaining resolution in diffusion weighted images, using a statistical reconstruction method that takes advantage of the high level of structural correlation observed in typical datasets. Compared to existing denoising methods, the proposed method performs reconstruction directly from the measured complex k-space data, allowing for gaussian noise modeling and theoretical characterizations of the resolution and signal-to-noise ratio of the reconstructed images. In addition, the proposed method is compatible with many different models of the diffusion signal (e.g., diffusion tensor modeling and q-space modeling). The joint reconstruction method can provide significant improvements in signal-to-noise ratio relative to conventional reconstruction techniques, with a relatively minor corresponding loss in image resolution. Results are shown in the context of diffusion spectrum imaging tractography and diffusion tensor imaging, illustrating the potential of this signal-to-noise ratio-enhancing joint reconstruction approach for a range of different diffusion imaging experiments.

Separate magnitude and phase regularization via compressed sensing

Compressed sensing (CS) has been used for accelerating magnetic resonance imaging acquisitions, but its use in applications with rapid spatial phase variations is challenging, e.g., proton resonance frequency shift (PRF-shift) thermometry and velocity mapping. Previously, an iterative MRI reconstruction with separate magnitude and phase regularization was proposed for applications where magnitude and phase maps are both of interest, but it requires fully sampled data and unwrapped phase maps. In this paper, CS is combined into this framework to reconstruct magnitude and phase images accurately from undersampled data. Moreover, new phase regularization terms are proposed to accommodate phase wrapping and to reconstruct images with encoded phase variations, e.g., PRF-shift thermometry and velocity mapping. The proposed method is demonstrated with simulated thermometry data and in vivo velocity mapping data and compared to conventional phase corrected CS.

Analytic image concept combined to SENSE reconstruction

OBJECT

Two approaches of reconstructing undersampled partial k-space data, acquired with multiple coils are compared: homodyne detection combined with SENSE (HM_SENSE) and analytic image reconstruction combined with SENSE (AI_SENSE). The latter overcomes limitations of HM_ SENSE by considering aliased images as analytic thus avoiding the need for phase correction required for HM_SENSE.

MATERIALS AND METHODS

In vivo imaging experiments were carried out in male Lewis rats using both gradient echo and spin echo sequences. Accelerated images obtained by using the various reconstruction algorithms were compared to fully sampled reference images both qualitatively and quantitatively.

RESULTS

For the various sampling patterns evaluated, both HM_SENSE and AI_SENSE were found to yield robust image reconstruction with small deviations from the reference image. Even for high acceleration factors AI_SENSE still provided useful results and was found superior compared to HM_SENSE.

CONCLUSION

Combination of partial k-space sampling and parallel image acquisition allows for further acceleration of data acquisition as compared to each method alone. Image reconstruction from undersampled data sets using the AI_SENSE algorithm was found to considerably reduce reconstruction errors and artifacts observed for HM_SENSE reconstruction caused by errors in phase estimation.

Self-calibrated multiple-echo acquisition with radial trajectories using the conjugate gradient method (SMART-CG)

PURPOSE

To remove phase inconsistencies between multiple echoes, an algorithm using a radial acquisition to provide inherent phase and magnitude information for self correction was developed. The information also allows simultaneous support for parallel imaging for multiple coil acquisitions.

MATERIALS AND METHODS

Without a separate field map acquisition, a phase estimate from each echo in multiple echo train was generated. When using a multiple channel coil, magnitude and phase estimates from each echo provide in vivo coil sensitivities. An algorithm based on the conjugate gradient method uses these estimates to simultaneously remove phase inconsistencies between echoes, and in the case of multiple coil acquisition, simultaneously provides parallel imaging benefits. The algorithm is demonstrated on single channel, multiple channel, and undersampled data.

RESULTS

Substantial image quality improvements were demonstrated. Signal dropouts were completely removed and undersampling artifacts were well suppressed.

CONCLUSION

The suggested algorithm is able to remove phase cancellation and undersampling artifacts simultaneously and to improve image quality of multiecho radial imaging, the important technique for fast three-dimensional MRI data acquisition.

Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations

Despite continuous hardware advances, MRI is frequently subject to field perturbations that are of higher than first order in space and thus violate the traditional k-space picture of spatial encoding. Sources of higher order perturbations include eddy currents, concomitant fields, thermal drifts, and imperfections of higher order shim systems. In conventional MRI with Fourier reconstruction, they give rise to geometric distortions, blurring, artifacts, and error in quantitative data. This work describes an alternative approach in which the entire field evolution, including higher order effects, is accounted for by viewing image reconstruction as a generic inverse problem. The relevant field evolutions are measured with a third-order NMR field camera. Algebraic reconstruction is then formulated such as to jointly minimize artifacts and noise in the resulting image. It is solved by an iterative conjugate-gradient algorithm that uses explicit matrix-vector multiplication to accommodate arbitrary net encoding. The feasibility and benefits of this approach are demonstrated by examples of diffusion imaging. In a phantom study, it is shown that higher order reconstruction largely overcomes variable image distortions that diffusion gradients induce in EPI data. In vivo experiments then demonstrate that the resulting geometric consistency permits straightforward tensor analysis without coregistration.

Constraining the initial phase in water-fat separation

An algorithm is described for use in chemical shift-based water-fat separation to constrain the phase of both species to be equal at an echo time of zero. This constraint is physically reasonable since the initial phase should be a property of the excitation pulse and receiver coil only. The advantages of phase constrained water-fat separation, namely, improved noise performance and/or reduced data requirements (fewer echos), are demonstrated in simulations and experiments.

POCS-enhanced correction of motion artifacts in parallel MRI

A new method for correction of MRI motion artifacts induced by corrupted k-space data, acquired by multiple receiver coils such as phased arrays, is presented. In our approach, a projections onto convex sets (POCS)-based method for reconstruction of sensitivity encoded MRI data (POCSENSE) is employed to identify corrupted k-space samples. After the erroneous data are discarded from the dataset, the artifact-free images are restored from the remaining data using coil sensitivity profiles. The error detection and data restoration are based on informational redundancy of phased-array data and may be applied to full and reduced datasets. An important advantage of the new POCS-based method is that, in addition to multicoil data redundancy, it can use a priori known properties about the imaged object for improved MR image artifact correction. The use of such information was shown to improve significantly k-space error detection and image artifact correction. The method was validated on data corrupted by simulated and real motion such as head motion and pulsatile flow.

Improved matrix inversion in image plane parallel MRI

A new 3D parallel magnetic resonance imaging (MRI) method named Generalized Unaliasing Incorporating Support constraint and sensitivity Encoding (GUISE) is presented. GUISE allows direct image recovery from arbitrary Cartesian k-space trajectories. However, periodic k-space sampling patterns are considered for reconstruction efficiency. Image recovery methods such as 2D SENSE (SENSitivity Encoding) and 2D CAIPIRINHA (Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration) are special instances of GUISE where specific restrictions are placed on the k-space sampling patterns used. It is shown that the sampling pattern has large impacts on the image reconstruction error due to noise. An efficient sampling pattern design method that incorporates prior knowledge of object support and coil sensitivity profile is proposed. It requires no experimental trials and could be used in clinical imaging. Comparison of the proposed sampling pattern design method with 2D SENSE and 2D CAIPIRINHA are made based on both simulation and experiment results. It is seen that this new adaptive sampling pattern design method results in a lower noise level in reconstructions due to better exploitation of the coil sensitivity variation and object support constraint. In addition, elimination of the non-object region from reconstruction potentially allows an acceleration factor higher than the number of receiver coils used.

Accelerated bilateral dynamic contrast-enhanced 3D spiral breast MRI using TSENSE

PURPOSE

To assess the ability of adaptive sensitivity encoding incorporating temporal filtering (TSENSE) to accelerate bilateral dynamic contrast-enhanced (DCE) 3D breast MRI.

MATERIALS AND METHODS

Bilateral DCE breast magnetic resonance imaging (MRI) exams were performed using a dual-band water-only excitation and a "stack-of-spirals" imaging trajectory. TSENSE was applied in the slab direction with an acceleration factor of 2. Four different techniques for sensitivity map calculation were compared by analyzing resultant contrast uptake curves qualitatively and quantitatively for 10 patient datasets. In addition, image quality and temporal resolution were compared between unaccelerated and TSENSE images.

RESULTS

TSENSE can increase temporal resolution by a factor of 2 in DCE imaging, providing better depiction of contrast uptake curves and good image quality. Of the different methods tested, calculation of static sensitivity maps by averaging late postcontrast frames yields the lowest aliasing artifact level based on ROI analysis.

CONCLUSION

TSENSE acceleration combined with 3D spiral imaging is very time-efficient, providing 11-second temporal resolution and 1.1 x 1.1 x 3 mm(3) spatial resolution over a 20 x 20 x 10 cm(3) field of view for each breast.

HASTE sequence with parallel acquisition and T2 decay compensation: application to carotid artery imaging

T2-weighted carotid artery images acquired using the turbo spin-echo (TSE) sequence frequently suffer from motion artifacts due to respiration and blood pulsation. The possibility of using HASTE sequence to achieve motion-free carotid images was investigated. The HASTE sequence suffers from severe blurring artifacts due to signal loss in later echoes due to T2 decay. Combining HASTE with parallel acquisition (PHASTE) decreases the number of echoes acquired and thus effectively reduces the blurring artifact caused by T2 relaxation. Further improvement in image sharpness can be achieved by performing T2 decay compensation before reconstructing the PHASTE data. Preliminary results have shown successful suppression of motion artifacts with PHASTE imaging. The image quality was enhanced relative to the original HASTE image, but was still less sharp than a non-motion-corrupted TSE image.

Improved image reconstruction for partial Fourier gradient-echo echo-planar imaging (EPI)

The partial Fourier gradient-echo echo planar imaging (EPI) technique makes it possible to acquire high-resolution functional MRI (fMRI) data at an optimal echo time. This technique is especially important for fMRI studies at high magnetic fields, where the optimal echo time is short and may not be achieved with a full Fourier acquisition scheme. In addition, it has been shown that partial Fourier EPI provides better anatomic resolvability than full Fourier EPI. However, the partial Fourier gradient-echo EPI may be degraded by artifacts that are not usually seen in other types of imaging. Those unique artifacts in partial Fourier gradient-echo EPI, to our knowledge, have not yet been systematically evaluated. Here we use the k-space energy spectrum analysis method to understand and characterize two types of partial Fourier EPI artifacts. Our studies show that Type 1 artifact, originating from k-space energy loss, cannot be corrected with pure postprocessing, and Type 2 artifact can be eliminated with an improved reconstruction method. We propose a novel algorithm, that combines images obtained from two or more reconstruction schemes guided by k-space energy spectrum analysis, to generate partial Fourier EPI with greatly reduced Type 2 artifact. Quality control procedures for avoiding Type 1 artifact in partial Fourier EPI are also discussed.

SENSE phase-constrained magnitude reconstruction with iterative phase refinement

Conventional sensitivity encoding (SENSE) reconstruction is based on equations in the complex domain. However, for many MRI applications only the magnitude is relevant. If there exists an estimate of the underlying phase information, a magnitude-only phase-constrained reconstruction can help to improve the conditioning of the SENSE reconstruction problem. Consequently, this reduces g-factor-related noise enhancement. In previous attempts at phase-constrained SENSE reconstruction, image quality was hampered by strong aliasing artifacts resulting from inadequate phase estimates and high sensitivity to phase errors. If a full-resolution phase image is used, a significant reduction in aliasing errors and better noise properties compared to SENSE can be obtained. An iterative scheme that improves the phase estimate to better approximate the phase is presented. The mathematical framework of the new approach is provided together with comparisons of conventional SENSE, phase-constrained SENSE, and the new phase-refinement method. Both theory and experimental verification demonstrate significantly better noise performance at high reduction factors, i.e., close to the theoretical limit. For applications that need only magnitude data, an iterative phase-constrained SENSE reconstruction can provide substantial SNR improvement over SENSE reconstruction and less artifacts than phase-constrained SENSE.

Parallel magnetic resonance imaging

Parallel imaging has been the single biggest innovation in magnetic resonance imaging in the last decade. The use of multiple receiver coils to augment the time consuming Fourier encoding has reduced acquisition times significantly. This increase in speed comes at a time when other approaches to acquisition time reduction were reaching engineering and human limits. A brief summary of spatial encoding in MRI is followed by an introduction to the problem parallel imaging is designed to solve. There are a large number of parallel reconstruction algorithms; this article reviews a cross-section, SENSE, SMASH, g-SMASH and GRAPPA, selected to demonstrate the different approaches. Theoretical (the g-factor) and practical (coil design) limits to acquisition speed are reviewed. The practical implementation of parallel imaging is also discussed, in particular coil calibration. How to recognize potential failure modes and their associated artefacts are shown. Well-established applications including angiography, cardiac imaging and applications using echo planar imaging are reviewed and we discuss what makes a good application for parallel imaging. Finally, active research areas where parallel imaging is being used to improve data quality by repairing artefacted images are also reviewed.

Optimization of sensitivity encoding with arbitrary k-space trajectories

Sensitivity encoding (SENSE) is a magnetic resonance technique that unifies gradient and receive coil encoding. SENSE reconstructs the image by solving a large, ill-conditioned inverse problem, which generally requires regularization and preconditioning. The present study suggests a simple heuristic for determining the regularization parameter. Also discussed are the use of density weighting and intensity correction as preconditioners and the role that coil sensitivity estimation has in regularization. A modification to the intensity correction is proposed for use with a phase constraint.

Dynamic magnetic resonance inverse imaging of human brain function

MRI is widely used for noninvasive hemodynamic-based functional brain imaging. In traditional spatial encoding, however, gradient switching limits the temporal resolution, which makes it difficult to unambiguously identify possible fast nonhemodynamic changes. In this paper we propose a novel reconstruction approach, called dynamic inverse imaging (InI), that is capable of providing millisecond temporal resolution when highly parallel detection is used. To achieve an order-of-magnitude speedup in generating time-resolved contrast estimates and dynamic statistical parametric maps (dSPMs), the spatial information is derived from an array of detectors rather than by time-consuming gradient-encoding methods. The InI approach was inspired by electroencephalography (EEG) and magnetoencephalography (MEG) source localization techniques. Dynamic MR InI was evaluated by means of numerical simulations. InI was also applied to measure BOLD hemodynamic time curves at 20-ms temporal resolution in a visual stimulation experiment using a 90-channel head array. InI is expected to improve the time resolution of MRI and provide increased flexibility in the trade-off between spatial and temporal resolution for studies of dynamic activation patterns in the human brain.

Magnetic resonance image reconstruction using equation system solving-based singularity function analysis

This paper presents a method of reconstructing magnetic resonance (MR) images from partial k-space using a so-called singularity function model. To estimate the parameters of the model, we propose a new technique based on equation system solving. The proposed reconstruction method is evaluated on both simulated and real brain MR data. It is also compared with existing techniques. The results show that this new strategy exhibits a great simplicity while offering a good reconstruction quality.