Motion-induced phase-corrected homodyne reconstruction for partial Fourier single-shot diffusion-weighted echo planar imaging of the liver

Partial Fourier encoding is popular in single-shot (ss) diffusion-weighted (DW) echo planar imaging (EPI) because it enables a shorter echo time (TE) and, hence, improves the signal-to-noise-ratio. Motion during diffusion encoding causes k-space shifting and dispersion, which compromises the quality of the homodyne reconstruction. This work provides a comprehensive understanding of the artifacts in homodyne reconstruction of partial Fourier ss-DW-EPI data in the presence of motion-induced phase and proposes the motion-induced phase-corrected homodyne (mpc-hdyne) reconstruction method to ameliorate these artifacts. Simulations with different types of motion-induced phase were performed to provide an understanding of the potential artifacts that occur in the homodyne reconstruction of partial Fourier ss-DW-EPI data. To correct for the artifacts, the mpc-hdyne reconstruction is proposed. The algorithm recenters k-space, updates the partial Fourier factor according to detected global k-space shifts, and removes low-resolution nonlinear phase before the conventional homodyne reconstruction. The mpc-hdyne reconstruction is tested on both simulation and in vivo data. Motion-induced phase can cause signal overestimation, worm artifacts, and signal loss in partial Fourier ss-DW-EPI data with the conventional homodyne reconstruction. Simulation and in vivo data showed that the proposed mpc-hdyne reconstruction ameliorated artifacts, yielding higher quality DW images compared with conventional homodyne reconstruction. Based on the understanding of the artifacts in homodyne reconstruction of partial Fourier ss-DW-EPI data, the mpc-hdyne reconstruction was proposed and showed superior performance compared with the conventional homodyne reconstruction on both simulation and in vivo data.

Partial Fourier reconstruction of complex MR images using complex-valued convolutional neural networks

PURPOSE

To provide a complex-valued deep learning approach for partial Fourier (PF) reconstruction of complex MR images.

METHODS

Conventional PF reconstruction methods, such as projection onto convex sets (POCS), uses low-resolution image phase information from the central symmetrically sampled k-space for image reconstruction. However, this smooth phase constraint undermines the phase estimation accuracy in presence of rapid local phase variations, causing image artifacts and limiting the extent of PF reconstruction. Using both magnitude and phase characteristics in big complex image datasets, we propose a complex-valued deep learning approach with an unrolled network architecture for PF reconstruction that iteratively reconstructs PF sampled data and enforces data consistency. We evaluate our approach for reconstructing both spin-echo and gradient-echo data.

RESULTS

The proposed method outperformed the iterative POCS PF reconstruction method. It produced better artifact suppression and recovery of both image magnitude and phase details in presence of local phase changes. No noise amplification was observed even for highly PF reconstruction. Moreover, the network trained on axial brain data could reconstruct sagittal and coronal brain and knee data. This method could be extended to 2D PF reconstruction and joint multi-slice PF reconstruction.

CONCLUSION

Our proposed method can effectively reconstruct MR data even at low PF fractions, yielding high-fidelity magnitude and phase images. It presents a valuable alternative to conventional PF reconstruction, especially for phase-sensitive 2D or 3D MRI applications.

Minimizing echo and repetition times in magnetic resonance imaging using a double half-echo k-space acquisition and low-rank reconstruction

Sampling k-space asymmetrically (ie, partial Fourier sampling) in the readout direction is a common way to reduce the echo time (TE) during magnetic resonance image acquisitions. This technique requires overlap around the center of k-space to provide a calibration region for reconstruction, which limits the minimum fractional echo to ~60% before artifacts are observed. The present study describes a method for reconstructing images from exact half echoes using two separate acquisitions with reversed readout polarity, effectively providing a full line of k-space without additional data around central k-space. This approach can benefit sequences or applications that prioritize short TE, short inter-echo spacing or short repetition time. An example of the latter is demonstrated to reduce banding artifacts in balanced steady-state free precession.

Partial Fourier reconstruction for improved resolution in 3D hyperpolarized 13 C EPI

PURPOSE

Asymmetric in-plane k-space sampling of EPI can reduce the minimum achievable TE in hyperpolarized 13 C with spectral-spatial radio frequency pulses, thereby reducing T 2 * weighting and signal-losses. Partial Fourier image reconstruction exploits the approximate Hermitian symmetry of k-space data and can be applied to asymmetric data sets to synthesize unmeasured data. Here we tested whether the application of partial Fourier image reconstruction would improve spatial resolution from hyperpolarized [1- 13 C ]pyruvate scans in the human brain.

METHODS

Fifteen healthy control subjects were imaged using a volumetric dual-echo echo-planar imaging sequence with spectral-spatial radio frequency excitation. Images were reconstructed by zero-filling as well as with the partial Fourier reconstruction algorithm projection-on-convex-sets. Resulting images were quantitatively evaluated with a no-reference image quality assessment.

RESULTS

The no-reference image sharpness metric agreed with perceived improvements in image resolution and contrast. The [1- 13 C ]lactate images benefitted most, followed by the [1- 13 C ]pyruvate images. The 13 C -bicarbonate images were improved by the smallest degree, likely owing to relatively lower SNR.

CONCLUSIONS

Partial Fourier imaging and reconstruction were shown to improve the sharpness and contrast of human HP 13 C brain data and is a viable method for enhancing resolution.

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.

Improving parallel imaging by jointly reconstructing multi-contrast data

PURPOSE

To develop parallel imaging techniques that simultaneously exploit coil sensitivity encoding, image phase prior information, similarities across multiple images, and complementary k-space sampling for highly accelerated data acquisition.

METHODS

We introduce joint virtual coil (JVC)-generalized autocalibrating partially parallel acquisitions (GRAPPA) to jointly reconstruct data acquired with different contrast preparations, and show its application in 2D, 3D, and simultaneous multi-slice (SMS) acquisitions. We extend the joint parallel imaging concept to exploit limited support and smooth phase constraints through Joint (J-) LORAKS formulation. J-LORAKS allows joint parallel imaging from limited autocalibration signal region, as well as permitting partial Fourier sampling and calibrationless reconstruction.

RESULTS

We demonstrate highly accelerated 2D balanced steady-state free precession with phase cycling, SMS multi-echo spin echo, 3D multi-echo magnetization-prepared rapid gradient echo, and multi-echo gradient recalled echo acquisitions in vivo. Compared to conventional GRAPPA, proposed joint acquisition/reconstruction techniques provide more than 2-fold reduction in reconstruction error.

CONCLUSION

JVC-GRAPPA takes advantage of additional spatial encoding from phase information and image similarity, and employs different sampling patterns across acquisitions. J-LORAKS achieves a more parsimonious low-rank representation of local k-space by considering multiple images as additional coils. Both approaches provide dramatic improvement in artifact and noise mitigation over conventional single-contrast parallel imaging reconstruction. Magn Reson Med 80:619-632, 2018. © 2018 International Society for Magnetic Resonance in Medicine.

Estimating absolute-phase maps using ESPIRiT and virtual conjugate coils

PURPOSE

To develop an ESPIRiT-based method to estimate coil sensitivities with image phase as a building block for efficient and robust image reconstruction with phase constraints.

THEORY AND METHODS

ESPIRiT is a new framework for calibration of the coil sensitivities and reconstruction in parallel magnetic resonance imaging. Applying ESPIRiT to a combined set of physical and virtual conjugate coils (VCC-ESPIRiT) implicitly exploits conjugate symmetry in k-space similar to VCC-GRAPPA. Based on this method, a new post-processing step is proposed for the explicit computation of coil sensitivities that include the absolute phase of the image. The accuracy of the computed maps is directly validated using a test based on projection onto fully sampled coil images and also indirectly in phase-constrained parallel-imaging reconstructions.

RESULTS

The proposed method can estimate accurate sensitivities which include low-resolution image phase. In case of high-frequency phase variations VCC-ESPIRiT yields an additional set of maps that indicates the existence of a high-frequency phase component. Taking this additional set of maps into account can improve the robustness of phase-constrained parallel imaging.

CONCLUSION

The extended VCC-ESPIRiT is a useful tool for phase-constrained imaging. Magn Reson Med 77:1201-1207, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Partial fourier and parallel MR image reconstruction with integrated gradient nonlinearity correction

PURPOSE

To describe how integrated gradient nonlinearity (GNL) correction can be used within noniterative partial Fourier (homodyne) and parallel (SENSE and GRAPPA) MR image reconstruction strategies, and demonstrate that performing GNL correction during, rather than after, these routines mitigates the image blurring and resolution loss caused by postreconstruction image domain based GNL correction.

METHODS

Starting from partial Fourier and parallel magnetic resonance imaging signal models that explicitly account for GNL, noniterative image reconstruction strategies for each accelerated acquisition technique are derived under the same core mathematical assumptions as their standard counterparts. A series of phantom and in vivo experiments on retrospectively undersampled data were performed to investigate the spatial resolution benefit of integrated GNL correction over conventional postreconstruction correction.

RESULTS

Phantom and in vivo results demonstrate that the integrated GNL correction reduces the image blurring introduced by the conventional GNL correction, while still correcting GNL-induced coarse-scale geometrical distortion. Images generated from undersampled data using the proposed integrated GNL strategies offer superior depiction of fine image detail, for example, phantom resolution inserts and anatomical tissue boundaries.

CONCLUSION

Noniterative partial Fourier and parallel imaging reconstruction methods with integrated GNL correction reduce the resolution loss that occurs during conventional postreconstruction GNL correction while preserving the computational efficiency of standard reconstruction techniques. Magn Reson Med 75:2534-2544, 2016. © 2015 Wiley Periodicals, Inc.

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

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