Robust high-quality multi-shot EPI with low-rank prior and machine learning
Berkin Bilgic1, Congyu Liao1, Mary Kate Manhard1, Qiyuan Tian1, Itthi Chatnuntawech2, Siddharth Srinivasan Iyer1, Stephen F Cauley1, Thorsten Feiweier3, Shivraman Giri4, Yuxin Hu5, Susie Y Huang1, Jonathan R Polimeni1, Lawrence L Wald1, and Kawin Setsompop1

1Martinos Center for Biomedical Imaging, Charlestown, MA, United States, 2National Nanotechnology Center, Pathum Thani, Thailand, 3Siemens Healthcare, Erlangen, Germany, 4Siemens Healthcare, Charlestown, MA, United States, 5Department of Electrical Engineering, Stanford University, Stanford, CA, United States


We introduce acquisition and reconstruction strategies for robust, high-quality multi-shot EPI (msEPI) without phase navigators. We extend the MUSSELS low-rank constrained parallel imaging technique to perform Virtual Coil (VC) reconstruction, and demonstrate diffusion imaging with sub-millimeter in-plane resolution using 55% partial-Fourier (PF) sampling. We propose Blip Up-Down Acquisition (BUDA) using interleaved blip-up and -down phase encoding, and incorporate B0 forward-modeling into MUSSELS to enable distortion- and navigator-free msEPI. We improve the acquisition efficiency by developing Simultaneous MultiSlice (SMS-)MUSSELS, and combine it with machine learning (ML) to provide Rtotal=16-fold acceleration with 3-shots. Deploying this in a spin-and-gradient-echo (SAGE) scan with signal modeling allows for whole-brain T2 and T2* mapping with high geometric fidelity in 12.5 seconds.


msEPI allows high-resolution imaging with reduced distortion, but combining shots is prohibitively difficult because of shot-to-shot phase variations. Existing navigator-free approaches employ parallel imaging (PI) to reconstruct each shot, from which phase variations are estimated (1,2). This imposes a limit on the distortion reduction since PI breaks down beyond Rinplane>4 acceleration.

MUSSELS (3) is a low-rank constrained PI approach (4,5) which improves acceleration capability, but requires a large number of shots (Rinplane=8 with 4-shots). We propose SMS-MUSSELS acquisition/reconstruction to further accelerate msEPI, demonstrate its extension to VC concept (6) and obtain high-quality images from a PF=55% acquisition. We propose Blip Up-Down Acquisition (buda) where msEPI sampling is performed with interleaved blip-up and -down acquisitions, and combine these shots with B0 forward-modeling and MUSSELS to yield distortion-free images. Finally, we push the acceleration to Rtotal=16 (RinplanexSMS=8x2) and combine ML and SMS-MUSSELS to obtain 1x1x3mm3 whole-brain T2 and T2* maps from a 12.5sec acquisition.

Code/data: https://bit.ly/2qzhA1t

Virtual Coil (VC-) MUSSELS

Acquisition: 0.85x0.85x3mm3 resolution diffusion data were acquired at b=1000s/mm2 using 32-channel reception at 3T with TE/TR=46/2000ms (7). 4-shots were collected at Rinplane=4 and PF=55%.

Reconstruction: In Fig1a, SENSE (8) was performed for each shot separately, followed by magnitude averaging over the 4-shots. MUSSELS in Fig1b was obtained via


where Ft is the undersampled Fourier operator in shot t, C are ESPIRiT sensitivities (9), and dt are the shot k-space data. H(x) enforces low-rank prior on the block-Hankel representation of the multi-shot data x, which is formed by concatenating the images xt from Ns shots. Proposed VC-MUSSELS (Fig1c) incorporates conjugate shot-images xt into the low-rank constraint, whereby conjugate-symmetric k-space helps estimate the missing data and improves the resolution (yellow boxes).

Blip Up-Down Acquisition (buda-) MUSSELS

Acquisition: 1x1x5mm3 spin-echo EPI at Rinplane=4 was acquired with TE/TR=75/3000ms, and two shots with blip-up and -down polarity were collected.

Reconstruction: Fig2a&b demonstrate separate SENSE for blip-up and -down acquisitions with significant distortion. Hybrid-space SENSE (10) jointly reconstructs the 2-shots by using their phase difference and B0 information from topup (9,10) (Fig2c). buda-MUSSELS obviates the need for phase estimation, and eliminates distortion by incorporating the fieldmap in PI to improve image quality and SNR (Fig2d, yellow boxes).

Network Estimated Artifacts for Tampered Reconstruction (NEATR) combines SMS-MUSSELS with ML

SMS-MUSSELS: is developed to combine MUSSELS with SMS using the readout-extended FOV concept (13). This represents SMS as undersampling in the kx-axis by concatenating the two slices along the readout (Fig3a). In-plane and slice acceleration could thus be captured using Ft with kx-ky undersampling and push the acceleration to RinplanexSMS=8x2 for spin-and-gradient echo (SAGE (14)) msEPI.

Due to high acceleration, SMS-MUSSELS failed to provide clean images using 3-shots (Rnet=16/3, Fig3a&4a). A network with U-Net architecture (15) was utilized to mitigate the SMS-MUSSELS artifacts. To provide “fully-sampled” data to train the network, four volunteers were scanned with 8-shots at prospective Rinplane=8 (FOV=224x224x120mm3, 1x1x3mm3 resolution, TEs=26/61/61/130/165ms, TR=8.3sec). MUSSELS reconstruction of this Rnet=1 data yielded references images.

Residual U-Net (Fig3b): learned a mapping between the 3-shot SMS-MUSSELS and the error relative to the reference images. Three volunteers’ data were used for training and the fourth subject was reserved for testing. U-Net with 5 levels, 2-loss, leaky-ReLU activation (16) and 64 filters at the highest level was trained on 64x64 patches. Real and imaginary parts of 3-shots were presented as channels for complex-valued processing.

Joint Virtual Coil (JVC-)SENSE: The refined U-Net magnitude munet allows us to solve for the phase of tth shot ϕt with wavelet (Ψ) regularization (17) (Fig3c):

Shot-phases from the complex U-Net reconstruction were used to initialize this non-convex problem. We finally solve for the magnitude using data from all shots by including the estimated phase variations in the sensitivities via Ceiϕt and create virtual coils Ceiϕt (Fig3d).

Results: Fig4 shows 2 echoes (out of 5) from a slice group where SMS-MUSSELS yielded 13.4% Rmse with ghosting/aliasing artifacts (arrows). U-Net mitigated these (8.7% error), allowing JVC-SENSE to provide clean images (7.6% Rmse). Using the SAGE signal equation yielded T2 and T2* maps with whole-brain coverage in 12.5 sec (Fig5).


We incorporated VC, buda and SMS concepts into MUSSELS to push the limits of PF, in-plane and slice acceleration in msEPI, and enabled high in-plane resolution, rapid structural imaging with improved geometric fidelity. SMS-NEATR took advantage of ML for accurate estimates of shot-to-shot phase variations and provided 1.8x Rmse reduction over SMS-MUSSELS. This paves the way for full synergistic combination of ML and model-based reconstruction, where deep learning could provide rapid estimates of B0 inhomogeneity to be included in buda-NEATR, and eliminate distortion without the need for topup processing.


This work was supported in part by NIH research grants: R01EB020613, R01EB019437, R24MH106096, P41EB015896, and the shared instrumentation grants: S10RR023401, S10RR019307, S10RR019254, S10RR023043.


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msEPI diffusion acquisition at b=1000s/mm2 with 0.85x0.85mm2 in-plane resolution using 4-shots. (a) Separate SENSE reconstructions for each of the Rinplane=4-fold accelerated shots were averaged after computing their magnitude. Missing data due to 55% partial-Fourier acquisition led to substantial resolution loss in the phase-encoding direction. (b) MUSSELS permitted joint reconstruction of the shots without navigation, but underestimated the missing portion of k-space with visible loss of resolution. (c) Proposed Virtual Coil MUSSELS made use of conjugate symmetry and seamlessly incorporated partial-Fourier into the joint reconstruction to improve the resolution (yellow boxes).

Blip-up and blip-down spin-echo EPI acquisitions at Rinplane=4 with 1x1mm2 in-plane resolution. (a&b) Performing separate SENSE reconstructions for the blip-up and -down acquisitions demonstrate severe geometric distortion at this lower slice, as well as voxel pile-ups and noise amplification. (c) Hybrid-space SENSE jointly reconstructs the 2-shots with B0 forward-modeling to eliminate distortion, but requires explicit phase-estimation and exhibits some noise amplification (yellow box). (d) Proposed buda-MUSSELS obviates the need for phase-navigation, eliminates distortion and improves reconstruction quality.

Due to high acceleration (Rtotal=16), proposed SMS-MUSSELS in (a) fails to provide clean reconstruction when the number of shots is reduced to 3. To amend this, we propose SMS-NEATR and synergistically combine machine learning and physics reconstruction. In (b), we use a complex-valued deep network to estimate and mitigate the artifacts in SMS-MUSSELS, and use the improved data to initialize the non-convex physics-based reconstruction in (c). This helps refine the phase estimates of each shot, which are then included in a final Joint Virtual Coil SENSE reconstruction to solve for a common magnitude image in (d).

(a) We have deployed our SMS-MUSSELS in the multi-contrast spin-and-gradient echo (SAGE) msEPI sequence with 5 echoes (first and last TEs are shown). Due to high acceleration (Rtotal=16), there were residual artifacts/ghosts (yellow arrows). (b) These were largely mitigated after the subsequent U-Net processing, at the cost of some image blurring. (c) Using the U-Net solution to initialize a final physics-based reconstruction provided further improvement in the SMS-NEATR result.

SMS-NEATR synergistically combines machine learning and physics-based reconstruction to enable T2 and T2* mapping with whole-brain coverage at 1x1x3mm3 resolution. While Rinplane=8-fold acceleration provides high geometric fidelity, SMS=2 acceleration reduces the TR to 4.2 seconds per shot, leading to a 12.5 second acquisition with 3-shots.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)