Vincent Jerome Schmithorst^{1} and Ashok Panigrahy^{1}

FFT-based reconstruction is suboptimal in the presence of signal decay during acquisition and between-excitation (shot-to-shot) variance in relaxation parameters. We present a novel reconstruction algorithm, Weighted Optimized Reconstruction of K-space (WORK), which weights each k-space point differently, optimizing for all sources of variance. Simulation results demonstrate the potential for 2X temporal SNR improvement in gradient-echo EPI acquisitions compared to standard FFT reconstruction while preserving spatial information. Substantial SNR improvement is also demonstrated for a pCASL 2D GE-EPI-SMS acquisition.

Simulation data was generated using routines in IDL. Parameters were taken to be comparable with a 64-X-64 2-D GE-EPI acquisition: dwell time = 0.5 ms, R2* = 28 Hz, ΔR2* = 0.7 Hz, ΔB0 = 0.1 Hz, thermal SNR = 500.

PCASL data was acquired on a normal adult volunteer using 2D GE-EPI with 4 X SMS acceleration on a Siemens 3T Skyra system. A FFT was performed and the slices unaliased. PCASL contrast (label-control) was computed. An inverse FFT was performed and the WORK algorithm performed using the k-space data. The WORK algorithm included line-by-line ghost correction and ΔB0 correction. pCASL contrast was again computed from the WORK reconstructed images.

The simulation results (Figures 1, 2) show that approximately 2X CNR improvement is available using the optimized WORK reconstruction. For the PCASL acquisition, there is excellent agreement between the pCASL contrasts (Figure 3), while the WORK technique displays substantial CNR gain (Figure 4). This implementation of WORK used the simulation values for R2* and ΔR2* for each voxel. Further improvement is evidently available via estimation of R2 and ΔR2* on a voxelwise basis.

Thus, WORK can provide substantial gain for 2D GE-EPI acquisitions with minimal computational cost. While background suppression is typically used to suppress R2* variation during a PCASL acquisition, our results show that substantial improvement is available even without background suppression, and our clinical experience in children shows that background suppression is less robust to patient motion.

This implementation of WORK is simplified such that only image data (magnitude/phase) need be acquired of the scanner instead of the raw data. This is the case for SMS acquisitions and also undersampled in-plane acquisitions, as the unaliasing occurs in the spatial and not the time dimension, so it may be done in a separate step.

The WORK algorithm may be extended to anatomical (e.g. non-dynamic) multi-shot acquisitions where there is shot-to-shot variance in relaxation parameters, such as T2-weighted FSE or T1-weighted MPRAGE sequences, as well as single-voxel spectroscopy and spectroscopic imaging. It may also be extended to sequences such as BOLD-EPI where the relaxation parameter is in the fact the variable of interest; in this case, the optimized reconstruction will more heavily weight the later-acquired datapoints. Further research will investigate the application of WORK to magnetic resonance fingerprinting (MRF) applications [2], as shot-to-shot parameter relaxation variance may also greatly affect the results.

[1] Setsompop K et al., Magn Reson Med 2012; 67(5): 1210-24.

[2] Ma D et al., Nature 2013; 495: 187-192.

[3] Fan Q et al., Brain Connect 2014; 4(9): 718–726.

Figure 1. As
proof-of-concept, a 64-point FID is simulated without any phase encoding (1000
repetitions). Left: Correctly
modeling the covariance due to shot-to-shot R2* variance results in an
estimator highly weighted towards the earlier time points which produces an
approximately 2X increase in temporal SNR.
Simulation repeated with misestimations of R2* and ΔR2*; Middle: results are quite robust
to underestimation of R2*; Right: results are robust to overestimation
of DR2*.

Figure 2. A 64-point
k-space acquisition is simulated with 40 voxels with magnitudes between 0.8 and
1.2. Top Left: The WORK algorithm
(dot-dashed line) results in an almost 2X increase in temporal SNR compared to
a standard FFT (solid line: deconvolved to account for spatial blurring due to
signal decay; dashed line: not deconvolved FFT); Top Right: the ground
truth voxel intensities are correctly recovered (expected since the WORK
estimator is unbiased); Bottom Left: The WORK estimator (20th
voxel; real component) is again weighted to earlier time points; Bottom
Right: Improvement available from WORK varies approximately linearly with
image SNR.

Figure 3. Comparison
of pCASL contrast from standard FFT-based reconstruction (top) and WORK (bottom)
from a normal adult volunteer using a 2D GE-SMS-EPI acquisition. Results show excellent agreement between the two
techniques.

Figure 4. The
relative improvement in T-score for the pCASL contrast produced via the WORK
reconstruction compared to the standard reconstruction for the acquisition
shown in Figure 3. Results show
substantial improvement throughout the image even with use in each voxel of the
R2* and ΔR2* values used for the simulations; further improvement is available
via voxelwise estimation.