Using the GRAPPA operator and the generalized sampling theorem to reconstruct undersampled non-Cartesian data

Self-calibrated interpolation of non-Cartesian data with GRAPPA in parallel imaging

PURPOSE

To develop a non-Cartesian k-space reconstruction method using self-calibrated region-specific interpolation kernels for highly accelerated acquisitions.

METHODS

In conventional non-Cartesian GRAPPA with through-time GRAPPA (TT-GRAPPA), the use of region-specific interpolation kernels has demonstrated improved reconstruction quality in dynamic imaging for highly accelerated acquisitions. However, TT-GRAPPA requires the acquisition of a large number of separate calibration scans. To reduce the overall imaging time, we propose Self-calibrated Interpolation of Non-Cartesian data with GRAPPA (SING) to self-calibrate region-specific interpolation kernels from dynamic undersampled measurements. The SING method synthesizes calibration data to adapt to the distinct shape of each region-specific interpolation kernel geometry, and uses a novel local k-space regularization through an extension of TT-GRAPPA. This calibration approach is used to reconstruct non-Cartesian images at high acceleration rates while mitigating noise amplification. The reconstruction quality of SING is compared with conjugate-gradient SENSE and TT-GRAPPA in numerical phantoms and in vivo cine data sets.

RESULTS

In both numerical phantom and in vivo cine data sets, SING offers visually and quantitatively similar reconstruction quality to TT-GRAPPA, and provides improved reconstruction quality over conjugate-gradient SENSE. Furthermore, temporal fidelity in SING and TT-GRAPPA is similar for the same acceleration rates. G-factor evaluation over the heart shows that SING and TT-GRAPPA provide similar noise amplification at moderate and high rates.

CONCLUSION

The proposed SING reconstruction enables significant improvement of acquisition efficiency for calibration data, while matching the reconstruction performance of TT-GRAPPA.

A GRAPPA algorithm for arbitrary 2D/3D non-Cartesian sampling trajectories with rapid calibration

PURPOSE

GRAPPA is a popular reconstruction method for Cartesian parallel imaging, but is not easily extended to non-Cartesian sampling. We introduce a general and practical GRAPPA algorithm for arbitrary non-Cartesian imaging.

METHODS

We formulate a general GRAPPA reconstruction by associating a unique kernel with each unsampled k-space location with a distinct constellation, that is, local sampling pattern. We calibrate these generalized kernels using the Fourier transform phase shift property applied to fully gridded or separately acquired Cartesian Autocalibration signal (ACS) data. To handle the resulting large number of different kernels, we introduce a fast calibration algorithm based on nonuniform FFT (NUFFT) and adoption of circulant ACS boundary conditions. We applied our method to retrospectively under-sampled rotated stack-of-stars/spirals in vivo datasets, and to a prospectively under-sampled rotated stack-of-spirals functional MRI acquisition with a finger-tapping task.

RESULTS

We reconstructed all datasets without performing any trajectory-specific manual adaptation of the method. For the retrospectively under-sampled experiments, our method achieved image quality (i.e., error and g-factor maps) comparable to conjugate gradient SENSE (cg-SENSE) and SPIRiT. Functional activation maps obtained from our method were in good agreement with those obtained using cg-SENSE, but required a shorter total reconstruction time (for the whole time-series): 3 minutes (proposed) vs 15 minutes (cg-SENSE).

CONCLUSIONS

This paper introduces a general 3D non-Cartesian GRAPPA that is fast enough for practical use on today's computers. It is a direct generalization of original GRAPPA to non-Cartesian scenarios. The method should be particularly useful in dynamic imaging where a large number of frames are reconstructed from a single set of ACS data.

Self-Calibrating Wave-Encoded Variable-Density Single-Shot Fast Spin Echo Imaging

BACKGROUND

It is highly desirable in clinical abdominal MR scans to accelerate single-shot fast spin echo (SSFSE) imaging and reduce blurring due to T₂ decay and partial-Fourier acquisition.

PURPOSE

To develop and investigate the clinical feasibility of wave-encoded variable-density SSFSE imaging for improved image quality and scan time reduction.

STUDY TYPE

Prospective controlled clinical trial.

SUBJECTS

With Institutional Review Board approval and informed consent, the proposed method was assessed on 20 consecutive adult patients (10 male, 10 female, range, 24-84 years).

FIELD STRENGTH/SEQUENCE

A wave-encoded variable-density SSFSE sequence was developed for clinical 3.0T abdominal scans to enable high acceleration (3.5×) with full-Fourier acquisitions by: 1) introducing wave encoding with self-refocusing gradient waveforms to improve acquisition efficiency; 2) developing self-calibrated estimation of wave-encoding point-spread function and coil sensitivity to improve motion robustness; and 3) incorporating a parallel imaging and compressed sensing reconstruction to reconstruct highly accelerated datasets.

ASSESSMENT

Image quality was compared pairwise with standard Cartesian acquisition independently and blindly by two radiologists on a scale from -2 to 2 for noise, contrast, confidence, sharpness, and artifacts. The average ratio of scan time between these two approaches was also compared.

STATISTICAL TESTS

A Wilcoxon signed-rank tests with a P value under 0.05 considered statistically significant.

RESULTS

Wave-encoded variable-density SSFSE significantly reduced the perceived noise level and improved the sharpness of the abdominal wall and the kidneys compared with standard acquisition (mean scores 0.8, 1.2, and 0.8, respectively, P < 0.003). No significant difference was observed in relation to other features (P = 0.11). An average of 21% decrease in scan time was achieved using the proposed method.

DATA CONCLUSION

Wave-encoded variable-density sampling SSFSE achieves improved image quality with clinically relevant echo time and reduced scan time, thus providing a fast and robust approach for clinical SSFSE imaging.

LEVEL OF EVIDENCE

1 Technical Efficacy: Stage 6 J. Magn. Reson. Imaging 2018;47:954-966.

Rotated stack-of-spirals partial acquisition for rapid volumetric parallel MRI

PURPOSE

We present a volumetric sampling method that rotates the spiral interleaves of a stack of spirals (SOSP) trajectory for reduced aliasing artifacts using parallel imaging with undersampling.

METHODS

The aliasing pattern in an undersampled SOSP acquisition was modified by consecutively rotating spiral interleaves in each phase-encoding plane. This allows a sampling scheme with a high reduction factor when using a volumetric multireceiver array. Phantom and in vivo brain images at a resolution of 1 × 1 × 2 mm(3) were acquired at 3T using a 32-channel coil. Images reconstructed with a reduction factor of 16 were compared for aliasing artifacts and geometry factor (g-factor).

RESULTS

Phantom and in vivo brain image results revealed that the rotated SOSP acquisition with a reduction factor of 16 produces images with reduced aliasing and lower g-factors than images acquired without rotation.

CONCLUSION

The proposed rotated SOSP sampling method is a highly efficient way to maximize the encoding power of volumetric receiver arrays in parallel imaging and is applicable to rapid volumetric scanning, including susceptibility-weighted imaging and functional MRI. Magn Reson Med 76:127-135, 2016. © 2015 Wiley Periodicals, Inc.

RARE/turbo spin echo imaging with Simultaneous Multislice Wave-CAIPI

PURPOSE

To enable highly accelerated RARE/Turbo Spin Echo (TSE) imaging using Simultaneous MultiSlice (SMS) Wave-CAIPI acquisition with reduced g-factor penalty.

METHODS

SMS Wave-CAIPI incurs slice shifts across simultaneously excited slices while playing sinusoidal gradient waveforms during the readout of each encoding line. This results in an efficient k-space coverage that spreads aliasing in all three dimensions to fully harness the encoding power of coil sensitivities. The novel MultiPINS radiofrequency (RF) pulses dramatically reduce the power deposition of multiband (MB) refocusing pulse, thus allowing high MB factors within the Specific Absorption Rate (SAR) limit.

RESULTS

Wave-CAIPI acquisition with MultiPINS permits whole brain coverage with 1 mm isotropic resolution in 70 s at effective MB factor 13, with maximum and average g-factor penalties of gmax  = 1.34 and gavg  = 1.12, and without √R penalty. With blipped-CAIPI, the g-factor performance was degraded to gmax  = 3.24 and gavg  = 1.42; a 2.4-fold increase in gmax relative to Wave-CAIPI. At this MB factor, the SAR of the MultiBand and PINS pulses are 4.2 and 1.9 times that of the MultiPINS pulse, while the peak RF power are 19.4 and 3.9 times higher.

CONCLUSION

Combination of the two technologies, Wave-CAIPI and MultiPINS pulse, enables highly accelerated RARE/TSE imaging with low SNR penalty at reduced SAR.

Wave-CAIPI for highly accelerated 3D imaging

PURPOSE

To introduce the wave-CAIPI (controlled aliasing in parallel imaging) acquisition and reconstruction technique for highly accelerated 3D imaging with negligible g-factor and artifact penalties.

METHODS

The wave-CAIPI 3D acquisition involves playing sinusoidal gy and gz gradients during the readout of each kx encoding line while modifying the 3D phase encoding strategy to incur interslice shifts as in 2D-CAIPI acquisitions. The resulting acquisition spreads the aliasing evenly in all spatial directions, thereby taking full advantage of 3D coil sensitivity distribution. By expressing the voxel spreading effect as a convolution in image space, an efficient reconstruction scheme that does not require data gridding is proposed. Rapid acquisition and high-quality image reconstruction with wave-CAIPI is demonstrated for high-resolution magnitude and phase imaging and quantitative susceptibility mapping.

RESULTS

Wave-CAIPI enables full-brain gradient echo acquisition at 1 mm isotropic voxel size and R = 3 × 3 acceleration with maximum g-factors of 1.08 at 3T and 1.05 at 7T. Relative to the other advanced Cartesian encoding strategies (2D-CAIPI and bunched phase encoding) wave-CAIPI yields up to two-fold reduction in maximum g-factor for nine-fold acceleration at both field strengths.

CONCLUSION

Wave-CAIPI allows highly accelerated 3D acquisitions with low artifact and negligible g-factor penalties, and may facilitate clinical application of high-resolution volumetric imaging.

Three-dimensional through-time radial GRAPPA for renal MR angiography

PURPOSE

To achieve high temporal and spatial resolution for contrast-enhanced time-resolved MR angiography exams (trMRAs), fast imaging techniques such as non-Cartesian parallel imaging must be used. In this study, the three-dimensional (3D) through-time radial generalized autocalibrating partially parallel acquisition (GRAPPA) method is used to reconstruct highly accelerated stack-of-stars data for time-resolved renal MRAs.

MATERIALS AND METHODS

Through-time radial GRAPPA has been recently introduced as a method for non-Cartesian GRAPPA weight calibration, and a similar concept can also be used in 3D acquisitions. By combining different sources of calibration information, acquisition time can be reduced. Here, different GRAPPA weight calibration schemes are explored in simulation, and the results are applied to reconstruct undersampled stack-of-stars data.

RESULTS

Simulations demonstrate that an accurate and efficient approach to 3D calibration is to combine a small number of central partitions with as many temporal repetitions as exam time permits. These findings were used to reconstruct renal trMRA data with an in-plane acceleration factor as high as 12.6 with respect to the Nyquist sampling criterion, where the lowest root mean squared error value of 16.4% was achieved when using a calibration scheme with 8 partitions, 16 repetitions, and a 4 projection × 8 read point segment size.

CONCLUSION

3D through-time radial GRAPPA can be used to successfully reconstruct highly accelerated non-Cartesian data. By using in-plane radial undersampling, a trMRA can be acquired with a temporal footprint less than 4s/frame with a spatial resolution of approximately 1.5 mm × 1.5 mm × 3 mm.

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

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

Fast MR image reconstruction for partially parallel imaging with arbitrary k-space trajectories

Both acquisition and reconstruction speed are crucial for magnetic resonance (MR) imaging in clinical applications. In this paper, we present a fast reconstruction algorithm for SENSE in partially parallel MR imaging with arbitrary k-space trajectories. The proposed method is a combination of variable splitting, the classical penalty technique and the optimal gradient method. Variable splitting and the penalty technique reformulate the SENSE model with sparsity regularization as an unconstrained minimization problem, which can be solved by alternating two simple minimizations: One is the total variation and wavelet based denoising that can be quickly solved by several recent numerical methods, whereas the other one involves a linear inversion which is solved by the optimal first order gradient method in our algorithm to significantly improve the performance. Comparisons with several recent parallel imaging algorithms indicate that the proposed method significantly improves the computation efficiency and achieves state-of-the-art reconstruction quality.

RT-GROG: parallelized self-calibrating GROG for real-time MRI

A real-time implementation of self-calibrating Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) operator gridding for radial acquisitions is presented. Self-calibrating GRAPPA operator gridding is a parallel-imaging-based, parameter-free gridding algorithm, where coil sensitivity profiles are used to calculate gridding weights. Self-calibrating GRAPPA operator gridding's weight-set calculation and image reconstruction steps are decoupled into two distinct processes, implemented in C++ and parallelized. This decoupling allows the weights to be updated adaptively in the background while image reconstruction threads use the most recent gridding weights to grid and reconstruct images. All possible combinations of two-dimensional gridding weights G(x)(m)G(y)(n) are evaluated for m,n = {-0.5, -0.4, ..., 0, 0.1, ..., 0.5} and stored in a look-up table. Consequently, the per-sample two-dimensional weights calculation during gridding is eliminated from the reconstruction process and replaced by a simple look-up table access. In practice, up to 34x faster reconstruction than conventional (parallelized) self-calibrating GRAPPA operator gridding is achieved. On a 32-coil dataset of size 128 x 64, reconstruction performance is 14.5 frames per second (fps), while the data acquisition is 6.6 fps.