A modified projection reconstruction trajectory for reduction of undersampling artifacts

PURPOSE: To reduce undersampling artifacts for a given number of repetitions of the projection reconstruction (PR) sequence by modifying its k-space trajectory to sample more mid-frequencies while reducing the sampling coverage of the peripheral spatial frequencies. MATERIALS AND METHODS: The single k-space spoke measured per repetition in the standard PR was modified so that one complete and two partial spokes were measured per repetition but with decreased k-space extent. The point spread functions (PSFs) and undersampling artifacts of the modified PR were compared with those of the standard PR for various numbers of projections. Phantom and in vivo images were used to assess the relative performance. RESULTS: PSF analysis indicated that the modified PR method provided reduced undersampling artifacts with somewhat reduced spatial resolution. The phantom and in vivo images corroborated this. CONCLUSION: The modified PR trajectory provides reduced undersampling artifact vs. the standard PR, particularly when the number of projections is limited and the artifact level is high.     

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.     

Undersampled projection-reconstruction imaging for time-resolved contrast-enhanced imaging.

In time-resolved contrast-enhanced 3D MR angiography, spatial resolution is traded for high temporal resolution. A hybrid method is presented that attempts to reduce this tradeoff in two of the spatial dimensions. It combines an undersampled projection acquisition in two dimensions with variable rate k-space sampling in the third. Spatial resolution in the projection plane is determined by readout resolution and is limited primarily by signal-to-noise ratio. Oversampling the center of k-space combined with temporal k-space interpolation provides time frames with minimal venous contamination. Results demonstrating improved resolution in phantoms and volunteers are presented using angular undersampling factors up to eight with acceptable projection reconstruction artifacts.     

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.     

Inversion recovery radial MRI with interleaved projection sets.

The radial trajectory has found applications in cardiac imaging because of its resilience to undersampling and motion artifacts. Recent work has shown that interleaved and weighted radial imaging can produce images with multiple contrasts from a single data set. This feature was investigated for inversion recovery imaging of scar using a radial technique. The 2D radial imaging method was modified to acquire quadruply interleaved projection sets within each acquisition window of the cardiac cycle. These data were reconstructed using k-space weightings that used a smaller segment of the acquisition window for the central k-space data, the determinant of image contrast. This method generates four images with different T1 weightings. The novel approach was compared with noninterleaved radial imaging, interleaved radial without weightings, and Cartesian imaging in simulations, phantoms, and seven subjects with clinical myocardial infarction. The results show that during a typical acquisition window after an inversion pulse, magnetization changes rapidly. The interleaved acquisition provided better image quality than the noninterleaved radial acquisition. Interleaving with weighting provided better quality when the inversion time (TI) was shorter than optimal; otherwise, interleaving without weighting was superior. These methods enable a radial trajectory to be employed in conjunction with preparation pulses for viability imaging.     

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.     

Optimizing spatiotemporal sampling for k-t BLAST and k-t SENSE: application to high-resolution real-time cardiac steady-state free precession.

In k-t BLAST and k-t SENSE, data acquisition is accelerated by sparsely sampling k-space over time. This undersampling in k-t space causes the object signals to be convolved with a point spread function in x-f space (x = spatial position, f = temporal frequency). The resulting aliasing is resolved by exploiting spatiotemporal correlations within the data. In general, reconstruction accuracy can be improved by controlling the k-t sampling pattern to minimize signal overlap in x-f space. In this work, we describe an approach to obtain generally favorable patterns for typical image series without specific knowledge of the image series itself. These optimized sampling patterns were applied to free-breathing, untriggered (i.e., real-time) cardiac imaging with steady-state free precession (SSFP). Eddy-current artifacts, which are otherwise increased drastically in SSFP by the undersampling, were minimized using alternating k-space sweeps. With the synergistic combination of the k-t approach with optimized sampling and SSFP with alternating k-space sweeps, it was possible to achieve a high signal-to-noise ratio, high contrast, and high spatiotemporal resolutions, while achieving substantial immunity against eddy currents. Cardiac images are shown, demonstrating excellent image quality and an in-plane resolution of approximately 2.0 mm at >25 frames/s, using one or more receiver coils.     

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.     

Importance of k-space trajectory in echo-planar myocardial tagging at rest and during dobutamine stress.

Hybrid fast gradient echo/echo-planar imaging (FGRE-EPI) can be used to increase temporal resolution, enhance tag contrast, and/or decrease scan time for breathhold myocardial tagging. However, off-resonance effects and motion can lead to local phase discontinuities in FGRE-EPI raw data when a conventional interleaved bottom-up k-space trajectory is used. These discontinuities can be particularly problematic for myocardial tagging, where the image energy is not only concentrated near the k-space origin, but is also concentrated in multiple spectral peaks centered throughout k-space. In this study, tag distortion artifacts in FGRE-EPI tagging due to off-resonance and velocity-induced phase discontinuities were characterized at rest and dobutamine stress, and the flyback and gradient moment smoothing (GMS) methods were shown to reduce these artifacts. For the specific parameters used in this study, flyback and GMS resulted in improved image quality at rest and stress, increased myocardium-tag contrast-to-noise ratio (11.4 +/- 2.1 vs. 10.0 +/- 2.9, P < 0.01 at rest; 11.1 +/- 1.8 vs. 8.1 +/- 2.4, P < 0.01 at stress), and reduced full width at half maximum of the tag profile (3.6 vs. 3.8 pixels at rest; 4.0 vs. 5.1 pixels at stress) compared to the conventional trajectory. A limitation of the improved trajectory is a parameter-dependent decrease in data acquisition efficiency. For the specific imaging protocol used, the repetition time of the improved trajectory increased by 36% compared to the conventional trajectory.     

Time-resolved undersampled projection reconstruction magnetic resonance imaging of the peripheral vessels using multi-echo acquisition.

The hybrid projection reconstruction (PR) imaging provides high temporal resolution through an undersampled PR acquisition for the in-plane dimensions and Cartesian slice encoding for the through-plane dimension. The undersampling of projection data introduces streak artifact, which may severely compromise image quality. This study reports on a combination of multi-echo acquisition with time-resolved undersampled PR imaging and its application to peripheral magnetic resonance angiography. Multi-echo acquisition improved imaging speed effectively, thereby reducing the undersampling streak artifact and improving the temporal resolution. The gradient distortion was reduced through gradient calibration and accurate k-space trajectory measurement.     

Generalized k-space decomposition with chemical shift correction for non-Cartesian water-fat imaging.

Chemical-shift artifacts associated with non-Cartesian imaging are more complex to model and less clinically acceptable than the bulk fat shift that occurs with conventional spin-warp Cartesian imaging. A novel k-space based iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) approach is introduced that decomposes multiple species while simultaneously correcting distortion of off-resonant species. The new signal model accounts for the additional phase accumulated by off-resonant spins at each point in the k-space acquisition trajectory. This phase can then be corrected by adjusting the decomposition matrix for each k-space point during the final IDEAL processing step with little increase in reconstruction time. The technique is demonstrated with water-fat decomposition using projection reconstruction (PR)/radial, spiral, and Cartesian spin-warp imaging of phantoms and human subjects, in each case achieving substantial correction of chemical-shift artifacts. Simulations of the point-spread-function (PSF) for off-resonant spins are examined to show the nature of the chemical-shift distortion for each acquisition. Also introduced is an approach to improve the signal model for species which have multiple resonant peaks. Many chemical species, including fat, have multiple resonant peaks, although such species are often approximated as a single peak. The improved multipeak decomposition is demonstrated with water-fat imaging, showing a substantial improvement in water-fat separation.     

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.     

Design of a logarithmic k-space spiral trajectory.

Spiral acquisitions are used in fast cardiac imaging because they traverse k-space efficiently and minimize flow artifacts. A variable pitch logarithmic spiral trajectory is designed to critically sample the low-frequency region in k-space and gradually undersample the high-frequency region. An approximate analytical expression for the trajectory provides a fast means to calculate the gradient waveforms and the sampled data points. A numerical method is introduced based on the trajectory curvature and the rate of change in the gradient magnitude with time for the composite Archimedean-logarithmic trajectory. The pulse sequence is implemented and images are acquired on phantoms and human hearts. The images show improved image resolution and some improvement in image quality as a result of increased extent in k-space and reduction in aliasing artifacts, respectively.     

Off-centered spiral trajectories.

The quality of spiral images depends on the accuracy of the k-space sampling locations. Although newer gradient systems can provide more accurate gradient waveforms, the sampling positions can be significantly distorted by timing misregistration between data acquisition and gradient systems. Even after the timing of data acquisition is tuned, minor residual errors can still cause shading artifacts which are problematic for quantitative MR applications such as phase-contrast flow quantitation. These timing errors can ideally be corrected by measuring the actual k-space trajectory, but trajectory measurement requires additional data acquisition and scan time. Therefore, off-centered spiral trajectories which are more robust against timing errors are proposed and applied to the phase-contrast method. The new trajectories turn shading artifacts into a slowly varying linear phase in reconstructed images without affecting the magnitude of images.     

Self-calibrated spiral SENSE.

Current standard sensitivity-encoded parallel imaging (SENSE) utilizes a fully sampled low-resolution reference scan to estimate the coil sensitivities. This reference scan adds scan time and may introduce misregistration artifacts. The purpose of this study was to investigate the feasibility of estimating the coil sensitivities for spiral SENSE directly from an undersampled k-space center. The limited spatial frequencies of the coil sensitivities, and the undersampling beyond the Nyquist radius cause image artifacts. A point spread function (PSF) analysis and experiments on both phantoms and humans identified an optimal radius for the k-space center by minimizing these image artifacts. The preliminary data indicate that self-calibrated SENSE is as accurate as standard SENSE, which uses a fully sampled reference scan.     

Fast four-dimensional coronary MR angiography with k-t GRAPPA

PURPOSE: To investigate the effectiveness of k-t GRAPPA for accelerating four-dimensional (4D) coronary MRA in comparison with GRAPPA and the feasibility of combining variable density undersampling with conventional k-t GRAPPA (k-t(2) GRAPPA) to alleviate the overhead of acquiring autocalibration signals. MATERIALS AND METHODS: The right coronary artery of nine healthy volunteers was scanned at 1.5 Tesla. The 4D k-space datasets were fully acquired and subsequently undersampled to simulate partially parallel acquisitions, namely, GRAPPA, k-t GRAPPA, and k-t(2) GRAPPA. Comparisons were made between the images reconstructed from full k-space datasets and those reconstructed from undersampled k-space datasets. RESULTS: k-t GRAPPA significantly reduced artifacts compared with GRAPPA and high acceleration factors were achieved with only minimal sacrifices in vessel depiction. k-t(2) GRAPPA could further increase imaging speed without significant losses in image quality. CONCLUSION: By exploiting high-degree spatiotemporal correlations during the rest period of a cardiac cycle, k-t GRAPPA and k-t(2) GRAPPA can greatly increase data acquisition efficiency and, therefore, are promising solutions for fast 4D coronary MRA.     

Improvement of spiral MRI with the measured k-space trajectory

The k-space trajectory of a spiral imaging sequence was measured with a self-encoding technique. The image quality improved dramatically when reconstructed with the measured k-space trajectory. There were substantial artifacts in images reconstructed with the derived k-space trajectory under the assumption of gradient system linearity. The results indicated the non-linearity of the gradient system and the effectiveness of the correction technique.     

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.     

Dynamic three-dimensional undersampled data reconstruction employing temporal registration.

Dynamic 3D imaging is needed for many applications such as imaging of the heart, joints, and abdomen. For these, the contrast and resolution that magnetic resonance imaging (MRI) offers are desirable. Unfortunately, the long acquisition time of MRI limits its application. Several techniques have been proposed to shorten the scan time by undersampling the k-space. To recover the missing data they make assumptions about the object's motion, restricting it in space, spatial frequency, temporal frequency, or a combination of space and temporal frequency. These assumptions limit the applicability of each technique. In this work we propose a reconstruction technique based on a weaker complementary assumption that restricts the motion in time. The technique exploits the redundancy of information in the object domain by predicting time frames from frames where there is little motion. The proposed method is well suited for several applications, in particular for cardiac imaging, considering that the heart remains relatively still during an important fraction of the cardiac cycle, or joint imaging where the motion can easily be controlled. This paper presents the new technique and the results of applying it to knee and cardiac imaging. The results show that the new technique can effectively reconstruct dynamic images acquired with an undersampling factor of 5. The resulting images suffer from little temporal and spatial blurring, significantly better than a sliding window reconstruction. An important attraction of the technique is that it combines reconstruction and registration, thus providing not only the 3D images but also its motion quantification. The method can be adapted to non-Cartesian k-space trajectories and nonuniform undersampling patterns.     

Centric ordering is superior to gradient moment nulling for motion artifact reduction in EPI

Echo-planar imaging (EPI) is sensitive to motion despite its rapid data acquisition rate. Compared with traditional imaging techniques, it is more sensitive to motion or flow in the phase-encode direction, which can cause image artifacts such as ghosting, misregistration, and loss of spatial resolution. Consequently, EPI of dynamic structures (eg, the cardiovascular system) could benefit from methods that eliminate these artifacts. In this paper, two methods of artifact reduction for motion in the phase-encode direction are evaluated. First, the k-space trajectory is evaluated by comparing centric with top-down ordered sequences. Next, velocity gradient moment nulling (GMN) of the phase-encode direction is evaluated for each trajectory. Computer simulations and experiments in flow phantoms and rabbits in vivo show that uncompensated centric ordering produces the highest image quality. This is probably due to a shorter readout duration, which reduces T2* relaxation losses and off-resonance effects, and to the linear geometry of phantoms and vessels, which can obscure centric blurring artifacts.