Reduced aliasing artifacts using variable-density k-space sampling trajectories.

A variable-density k-space sampling method is proposed to reduce aliasing artifacts in MR images. Because most of the energy of an image is concentrated around the k-space center, aliasing artifacts will contain mostly low-frequency components if the k-space is uniformly undersampled. On the other hand, because the outer k-space region contains little energy, undersampling that region will not contribute severe aliasing artifacts. Therefore, a variable-density trajectory may sufficiently sample the central k-space region to reduce low-frequency aliasing artifacts and may undersample the outer k-space region to reduce scan time and to increase resolution. In this paper, the variable-density sampling method was implemented for both spiral imaging and two-dimensional Fourier transform (2DFT) imaging. Simulations, phantom images and in vivo cardiac images show that this method can significantly reduce the total energy of aliasing artifacts. In general, this method can be applied to all types of k-space sampling trajectories.     

Time-resolved contrast-enhanced imaging with isotropic resolution and broad coverage using an undersampled 3D projection trajectory.

Time-resolved contrast-enhanced 3D MR angiography (MRA) methods have gained in popularity but are still limited by the tradeoff between spatial and temporal resolution. A method is presented that greatly reduces this tradeoff by employing undersampled 3D projection reconstruction trajectories. The variable density k-space sampling intrinsic to this sequence is combined with temporal k-space interpolation to provide time frames as short as 4 s. This time resolution reduces the need for exact contrast timing while also providing dynamic information. Spatial resolution is determined primarily by the projection readout resolution and is thus isotropic across the FOV, which is also isotropic. Although undersampling the outer regions of k-space introduces aliased energy into the image, which may compromise resolution, this is not a limiting factor in high-contrast applications such as MRA. Results from phantom and volunteer studies are presented demonstrating isotropic resolution, broad coverage with an isotropic field of view (FOV), minimal projection reconstruction artifacts, and temporal information. In one application, a single breath-hold exam covering the entire pulmonary vasculature generates high-resolution, isotropic imaging volumes depicting the bolus passage.     

Reconstruction of undersampled non-Cartesian data sets using pseudo-Cartesian GRAPPA in conjunction with GROG.

Most k-space-based parallel imaging reconstruction techniques, such as Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), necessitate the acquisition of regularly sampled Cartesian k-space data to reconstruct a nonaliased image efficiently. However, non-Cartesian sampling schemes offer some inherent advantages to the user due to their better coverage of the center of k-space and faster acquisition times. On the other hand, these sampling schemes have the disadvantage that the points acquired generally do not lie on a grid and have complex k-space sampling patterns. Thus, the extension of Cartesian GRAPPA to non-Cartesian sequences is nontrivial. This study introduces a simple, novel method for performing Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG (GRAPPA Operator Gridding) to arrive at a nonaliased image. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. This flexibility in terms of both the appearance and number of patterns allows this pseudo-Cartesian GRAPPA to be used with undersampled data sets acquired with any non-Cartesian trajectory. The successful implementation of the reconstruction algorithm using several different trajectories, including radial, rosette, spiral, one-dimensional non-Cartesian, and zig-zag trajectories, is demonstrated.     

Polar sampling in k-space: Reconstruction effects

Magnetic resonance images are most commonly computed by taking the inverse Fourier transform of the k-space data. This transformation can potentially create artifacts in the im age, depending on the reconstruction algorithm used. For equally spaced radial and azimuthal k-space polar sampling, both gridding and convolution backprojection are applicable. However, these algorithms potentially can yield different res olution, signal-to-noise ratio, and aliasing characteristics in the reconstructed image. Here, these effects are analyzed and their tradeoffs are discussed. It is shown that, provided the modulation transfer function and the signal-to-noise ratio are considered together, these algorithms perform similarly. In contrast, their aliasing behavior is different, since their re spective point spread functions (PSF) differ. In gridding, the PSF is composed of the mainlobe and ringlobes that lead to aliasing. Conversely, there are no ringlobes in the convolution backprojection PSF, thus radial aliasing effects are mini mized. Also, a hybrid gridding and convolution backprojection reconstruction is presented for radially nonequidistant k-space polar sampling.     

Improving GRAPPA using cross-sampled autocalibration data

In conventional generalized autocalibrating partially parallel acquisitions, the autocalibration signal (ACS) lines are acquired with a frequency-encoding direction in parallel to other undersampled lines. In this study, a cross sampling method is proposed to acquire the ACS lines orthogonal to the undersampled lines. This cross sampling method increases the amount of calibration data along the direction, where k-space is undersampled, and especially improves the calibration accuracy when a small number of ACS lines are acquired. The cross sampling method is implemented with swapped frequency and phase encoding gradients. In addition, an iterative coregistration method is also developed to correct the inconsistency between the ACS and undersampled data, which are acquired separately in two orthogonal directions. The same calibration and reconstruction procedure as conventional generalized autocalibrating partially parallel acquisitions is then applied to the corrected data to recover the unacquired k-space data and obtain the final image. Reconstruction results from simulations, phantom and in vivo human brain experiments have distinctly demonstrated that the proposed method, named cross-sampled generalized autocalibrating partially parallel acquisitions, can effectively reduce the aliasing artifacts of conventional generalized autocalibrating partially parallel acquisitions when very few ACS lines are acquired, especially at high outer k-space reduction factors.     

Fast method for 1D non-cartesian parallel imaging using GRAPPA.

MRI with non-Cartesian sampling schemes can offer inherent advantages. Radial acquisitions are known to be very robust, even in the case of vast undersampling. This is also true for 1D non-Cartesian MRI, in which the center of k-space is oversampled or at least sampled at the Nyquist rate. There are two main reasons for the more relaxed foldover artifact behavior: First, due to the oversampling of the center, high-energy foldover artifacts originating from the center of k-space are avoided. Second, due to the non-equidistant sampling of k-space, the corresponding field of view (FOV) is no longer well defined. As a result, foldover artifacts are blurred over a broad range and appear less severe. The more relaxed foldover artifact behavior and the densely sampled central k-space make trajectories of this type an ideal complement to autocalibrated parallel MRI (pMRI) techniques, such as generalized autocalibrating partially parallel acquisitions (GRAPPA). Although pMRI can benefit from non-Cartesian trajectories, this combination has not yet entered routine clinical use. One of the main reasons for this is the need for long reconstruction times due to the complex calculations necessary for non-Cartesian pMRI. In this work it is shown that one can significantly reduce the complexity of the calculations by exploiting a few specific properties of k-space-based pMRI.     

Parallel MR imaging

Parallel imaging is a robust method for accelerating the acquisition of magnetic resonance imaging (MRI) data, and has made possible many new applications of MR imaging. Parallel imaging works by acquiring a reduced amount of k-space data with an array of receiver coils. These undersampled data can be acquired more quickly, but the undersampling leads to aliased images. One of several parallel imaging algorithms can then be used to reconstruct artifact-free images from either the aliased images (SENSE-type reconstruction) or from the undersampled data (GRAPPA-type reconstruction). The advantages of parallel imaging in a clinical setting include faster image acquisition, which can be used, for instance, to shorten breath-hold times resulting in fewer motion-corrupted examinations. In this article the basic concepts behind parallel imaging are introduced. The relationship between undersampling and aliasing is discussed and two commonly used parallel imaging methods, SENSE and GRAPPA, are explained in detail. Examples of artifacts arising from parallel imaging are shown and ways to detect and mitigate these artifacts are described. Finally, several current applications of parallel imaging are presented and recent advancements and promising research in parallel imaging are briefly reviewed.     

Reduced field of view and undersampled PR combined for interventional imaging of a fully dynamic field of view.

Active catheter imaging was investigated using real-time undersampled projection reconstruction (PR) combined with the temporal filtering technique of reduced field of view (rFOV). Real-time rFOV processing was interactively enabled during highly undersampled catheter imaging, resulting in improved artifact suppression with better temporal resolution than that obtained by view-sharing. Imaging with 64 to 32 projections provided a resolution of 2 x 2 x 8 mm, and four to eight true frames per second. Image artifacts were reduced when rFOV processing was applied to the undersampled images. A comparison with Cartesian rFOV showed that PR image quality is less susceptible to aliasing that results from rFOV imaging with a wholly dynamic outer FOV. Simulations and MRI experiments demonstrated that PR rFOV provides significant artifact suppression, even for a fully dynamic FOV. The near doubling of temporal resolution that is possible with PR rFOV permits accurate monitoring of highly dynamic events, such as catheter movements, and arrhythmias, such as ventricular ectopy.     

Retrospective motion compensation using variable-density spiral trajectories

PURPOSE: To develop a method of retrospectively correcting for motion artifacts using a variable-density spiral (VDS) trajectory. MATERIALS AND METHODS: Each VDS interleaf was designed to adequately sample the same center region of k-space. This central overlapping region can then be used to measure rigid body motion between the acquisition of each VDS interleaf. By applying appropriate phase shifts and rotations of the k-space data, rigid body motion artifacts can be removed, resulting in images with less motion corruption. RESULTS: Both phantom and volunteer experiments are shown, demonstrating the technique's ability to further reduce artifacts in images acquired with an already motion-resistant acquisition trajectory. Registration accuracy is highly dependent on the trajectory design parameters. This space was explored to find an optimal design of VDS trajectories for motion compensation. CONCLUSION: Using appropriately designed VDS trajectories, residual motion artifacts can be significantly reduced by retrospectively correcting for in-plane rigid body motion. An overlapping region of approximately 8% of the central region of k-space and approximately 70 interleaves were found to be near-optimal parameters for retrospective correction using VDS trajectories.     

Fast 3D imaging using variable-density spiral trajectories with applications to limb perfusion.

Variable-density k-space sampling using a stack-of-spirals trajectory is proposed for ultra fast 3D imaging. Since most of the energy of an image is concentrated near the k-space origin, a variable-density k-space sampling method can be used to reduce the sampling density in the outer portion of k-space. This significantly reduces scan time while introducing only minor aliasing artifacts from the low-energy, high-spatial-frequency components. A stack-of-spirals trajectory allows control over the density variations in both the k(x)-k(y) plane and the k(z) direction while fast k-space coverage is provided by spiral trajectories in the k(x)-k(y) plane. A variable-density stack-of-spirals trajectory consists of variable-density spirals in each k(x)-k(y) plane that are located in varying density in the k(z) direction. Phantom experiments demonstrate that reasonable image quality is preserved with approximately half the scan time. This technique was then applied to first-pass perfusion imaging of the lower extremities which demands very rapid volume coverage. Using a variable-density stack-of-spirals trajectory, 3D images were acquired at a temporal resolution of 2.8 sec over a large volume with a 2.5 x 2.5 x 8 mm(3) spatial resolution. These images were used to resolve the time-course of muscle intensity following contrast injection.     

Decomposed direct matrix inversion for fast non-cartesian SENSE reconstructions.

A new k-space direct matrix inversion (DMI) method is proposed here to accelerate non-Cartesian SENSE reconstructions. In this method a global k-space matrix equation is established on basic MRI principles, and the inverse of the global encoding matrix is found from a set of local matrix equations by taking advantage of the small extension of k-space coil maps. The DMI algorithm's efficiency is achieved by reloading the precalculated global inverse when the coil maps and trajectories remain unchanged, such as in dynamic studies. Phantom and human subject experiments were performed on a 1.5T scanner with a standard four-channel phased-array cardiac coil. Interleaved spiral trajectories were used to collect fully sampled and undersampled 3D raw data. The equivalence of the global k-space matrix equation to its image-space version, was verified via conjugate gradient (CG) iterative algorithms on a 2x undersampled phantom and numerical-model data sets. When applied to the 2x undersampled phantom and human-subject raw data, the decomposed DMI method produced images with small errors (< or = 3.9%) relative to the reference images obtained from the fully-sampled data, at a rate of 2 s per slice (excluding 4 min for precalculating the global inverse at an image size of 256 x 256). The DMI method may be useful for noise evaluations in parallel coil designs, dynamic MRI, and 3D sodium MRI with fixed coils and trajectories.     

Non‐Cartesian parallel imaging reconstruction

Non‐Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non‐Cartesian trajectories can enable more efficient coverage of k‐space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be used to reconstruct images from undersampled Cartesian data, non‐Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the nonhomogeneous sensitivities of multi‐coil phased arrays. This review will begin with an overview of non‐Cartesian k‐space trajectories and their sampling properties, followed by an in‐depth discussion of several selected non‐Cartesian parallel imaging algorithms. Three representative non‐Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non‐Cartesian generalized autocalibrating partially parallel acquisition (GRAPPA), and Iterative Self‐Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non‐Cartesian parallel imaging will be covered. J. Magn. Reson. Imaging 2014;40:1022–1040 . © 2014 Wiley Periodicals, Inc.     

Coronary MRA with 3D undersampled projection reconstruction TrueFISP.

Undersampled projection reconstruction (PR) offers improved imaging efficiency allowing a relative tradeoff between signal-to-noise ratio (SNR) or streak artifact and the number of acquired k-space views rather than the tradeoff between resolution or aliasing artifact and the number of acquired k-space lines inherent to Fourier imaging techniques. TrueFISP (true fast imaging with steady state precession) is ideally suited for undersampled PR imaging because of its inherently high SNR. The purpose of this work was to investigate the feasibility of using undersampled three-dimensional (3D) PR TrueFISP for breathhold coronary artery imaging. Phantom studies and a preliminary in vivo comparison demonstrated the improved spatial resolution of PR over Fourier TrueFISP with the same imaging time. In a 24-heartbeat coronary imaging scheme, segmented 3D PR TrueFISP provided a 1.0 x 1.0 mm(2) isotropic in-plane voxel size while acquiring between 93 and 153 views per partition. Streak artifacts were present in some images but were not found to impede coronary artery delineation. In conclusion, 3D undersampled PR TrueFISP provides isotropic in-plane voxel size within a single breathhold and is a promising technique for coronary artery imaging.     

Sparse MRI: The application of compressed sensing for rapid MR imaging.

The sparsity which is implicit in MR images is exploited to significantly undersample k-space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain-for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressed-sensing, images with a sparse representation can be recovered from randomly undersampled k-space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the l(1) norm of a transformed image, subject to data fidelity constraints. Examples demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin-echo brain imaging and 3D contrast enhanced angiography.     

Three-dimensional MRI with an undersampled spherical shells trajectory.

The shells trajectory is a 3D data acquisition method with improved efficiency compared to Cartesian sampling. It is a true center-out trajectory that does not repeatedly resample the center of k-space, and also offers advantages for motion correction. This work demonstrates that k-space undersampling can be combined with the shells trajectory to further accelerate the acquisition. The undersampling was implemented by removing selected interleaves from shells with larger radii. Because only the outer portion of k-space was undersampled, the artifacts introduced were of low energy and high spatial frequency. The undersampling rate was determined by a Kaiser window with a variable shape parameter beta. Various undersampling schemes with different beta values were examined. Phantom and volunteer studies demonstrate that when up to a twofold acceleration is achieved, only minor artifacts are introduced by undersampling the shells trajectory. For a fixed acquisition time, the improved efficiency can be used to increase spatial resolution.     

The influence of radial undersampling schemes on compressed sensing reconstruction in breast MRI

Fast imaging applications in magnetic resonance imaging (MRI) frequently involve undersampling of k‐space data to achieve the desired temporal resolution. However, high temporal resolution images generated from undersampled data suffer from aliasing artifacts. In radial k‐space sampling, this manifests as undesirable streaks that obscure image detail. Compressed sensing reconstruction has been shown to reduce such streak artifacts, based on the assumption of image sparsity. Here, compressed sensing is implemented with three different radial sampling schemes (golden‐angle, bit‐reversed, and random sampling), which are compared over a range of spatiotemporal resolutions. The sampling methods are implemented in static scenarios where different undersampling patterns could be compared. Results from point spread function studies, simulations, phantom and in vivo experiments show that the choice of radial sampling pattern influences the quality of the final image reconstructed by the compressed sensing algorithm. While evenly undersampled radial trajectories are best for specific temporal resolutions, golden‐angle radial sampling results in the least overall error when various temporal resolutions are considered. Reduced temporal fluctuations from aliasing artifacts in golden‐angle sampling translates to improved compressed sensing reconstructions overall. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.     

Reconstruction after rotational motion.

Patient rotational motion during a scan causes the k-space sampling to be both irregular and undersampled. Conventional regridding requires an estimate of the sampling density at each measured point and is not strictly consistent with sampling theory. Here, a 2D problem is converted to a series of 1D regriddings by exact interpolation along the measured readouts. Each 1D regridding, expressed in matrix form, requires a matrix inversion to gain an exact solution. Undersampled regions make the matrix ill-conditioned but summing the matrix columns (without inversion) indicates the undersampled regions. The missing data could be reacquired, but in this study it is estimated using a Delaunay triangle-based linear interpolation on the original 2D data. The matrix conditioning is improved, leading to images with reduced artifacts compared to other regridding schemes. Furthermore, there is no requirement to estimate a density compensation function at each of the measured points.     

k-space undersampling in PROPELLER imaging.

PROPELLER MRI (periodically rotated overlapping parallel lines with enhanced reconstruction) provides images with significantly fewer B(0)-related artifacts than echo-planar imaging (EPI), as well as reduced sensitivity to motion compared to conventional multiple-shot fast spin-echo (FSE). However, the minimum imaging time in PROPELLER is markedly longer than in EPI and 50% longer than in conventional multiple-shot FSE. Often in MRI, imaging time is reduced by undersampling k-space. In the present study, the effects of undersampling on PROPELLER images were evaluated using simulated and in vivo data sets. Undersampling using PROPELLER patterns with reduced number of samples per line, number of lines per blade, or number of blades per acquisition, while maintaining the same k-space field of view (FOV(k)) and uniform sampling at the edges of FOV(k), reduced imaging time but led to severe image artifacts. In contrast, undersampling by means of removing whole blades from a PROPELLER sampling pattern that sufficiently samples k-space produced only minimal image artifacts, mainly manifested as blurring in directions parallel to the blades removed, even when reducing imaging time by as much as 50%. Finally, undersampling using asymmetric blades and taking advantage of Hermitian symmetries to fill-in the missing data significantly reduced imaging time without causing image artifacts.     

Aliasing artifacts with the BLADE technique: causes and effective suppression

Purpose:

To elucidate the causes of aliasing artifacts with the BLADE technique and clarify the effective suppression methods.

Materials and Methods:

We separately observed the aliasing artifacts of BLADE from features inside and then outside the defined field‐of‐view (FOV) using phantom studies. The effectiveness of suppressing them with phase oversampling (POS) and presaturation pulses (SAT) was evaluated. Finally, our observations were confirmed for a healthy volunteer.

Results:

Characteristic aliasing artifacts were observed from both inside and outside the FOV. Those from inside the FOV were sufficiently suppressed by using a POS of 25%, considering the acquisition time prolongation. Those from outside the FOV were nearly suppressed using SAT outside the FOV without selecting needless receiver coils. Aliasing artifacts on the coronal images of the head and neck with a healthy volunteer were completely suppressed by a combination of using a POS of 25% and using SAT on all four sides outside the FOV.

Conclusion:

The characteristic aliasing artifacts of BLADE are caused from both inside and outside the defined FOV. They can be effectively suppressed by a combination of using a POS of 25% and using SAT on all four sides outside the FOV. J. Magn. Reson. Imaging 2011;33:432–440. © 2011 Wiley‐Liss, Inc.     

Isotropic submillimeter fMRI in the human brain at 7 T: Combining reduced field-of-view imaging and partially parallel acquisitions

Echo‐planar imaging is the most widely used imaging sequence for functional magnetic resonance imaging (fMRI) due to its fast acquisition. However, it is prone to local distortions, image blurring, and signal voids. As these effects scale with echo train length and field strength, it is essential for high‐resolution echo‐planar imaging at ultrahigh field to address these problems. Partially parallel acquisition methods can be used to improve the image quality of echo‐planar imaging. However, partially parallel acquisition can be affected by aliasing artifacts and noise enhancement. Another way to shorten the echo train length is to reduce the field‐of‐view (FOV) while maintaining the same spatial resolution. However, to achieve significant acceleration, the resulting FOV becomes very small. Another problem occurs when FOV selection is incomplete such that there is remaining signal aliased from the region outside the reduced FOV. In this article, a novel approach, a combination of reduced FOV imaging with partially parallel acquisition, is presented. This approach can address the problems described above of each individual method, enabling high‐quality single‐shot echo‐planar imaging acquisition, with submillimeter isotropic resolution and good signal‐to‐noise ratio, for fMRI at ultrahigh field strength. This is demonstrated in fMRI of human brain at 7T with an isotropic resolution of 650 μm. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.