Berkin Bilgic^{1}, Congyu Liao^{1}, Mary Kate Manhard^{1}, Qiyuan Tian^{1}, Itthi Chatnuntawech^{2}, Siddharth Srinivasan Iyer^{1}, Stephen F Cauley^{1}, Thorsten Feiweier^{3}, Shivraman Giri^{4}, Yuxin Hu^{5}, Susie Y Huang^{1}, Jonathan R Polimeni^{1}, Lawrence L Wald^{1}, and Kawin Setsompop^{1}

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 B_{0} 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 R_{total}=16-fold acceleration
with 3-shots. Deploying this in a spin-and-gradient-echo (SAGE) scan with signal
modeling allows for whole-brain T_{2} and T_{2}* 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 R_{inplane}>4 acceleration.

MUSSELS (3) is a low-rank constrained PI approach (4,5) which
improves acceleration capability, but requires a large number of
shots (R_{inplane}=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 B_{0} forward-modeling
and MUSSELS to yield distortion-free images. Finally, we push
the acceleration to R_{total}=16 (R_{inplane}xSMS=8x2) and
combine ML and SMS-MUSSELS to obtain 1x1x3mm^{3} whole-brain
T_{2} and T_{2}* maps from a 12.5sec acquisition.

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

Acquisition:
0.85x0.85x3mm^{3} resolution diffusion data were acquired at
b=1000s/mm^{2} using 32-channel reception at 3T with
TE/TR=46/2000ms (7). 4-shots were collected at R_{inplane}=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

$$mi{n}_{x}\sum _{t=1}^{{N}_{s}}\parallel {F}_{t}C{x}_{t}-{d}_{t}{\parallel}_{2}^{2}+\lambda \parallel H\left(x\right){\parallel}_{\ast}$$

where ${F}_{t}$ is the undersampled Fourier operator in shot $t$, $C$ are ESPIRiT sensitivities (9), and ${d}_{t}$ are the
shot k-space data. $\parallel H\left(x\right){\parallel}_{\ast}$ enforces low-rank
prior on the block-Hankel representation of the multi-shot data $x$, which is formed by concatenating the images ${x}_{t}$ from ${N}_{s}$ shots. Proposed
VC-MUSSELS (*Fig1c*) incorporates
conjugate shot-images ${x}_{t}^{\ast}$ 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: 1x1x5mm^{3} spin-echo EPI at R_{inplane}=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 B_{0} 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 *k _{x}-*axis by
concatenating the two slices along the

Due to high acceleration, SMS-MUSSELS
failed to provide clean images using 3-shots (R_{net}=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*
R_{inplane}=8 (FOV=224x224x120mm^{3}, 1x1x3mm^{3}
resolution, TEs=26/61/61/130/165ms, TR=8.3sec). MUSSELS reconstruction of this
R_{net}=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, ${\ell}_{2}$-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 ${m}_{unet}$ allows us to solve for the phase of ${t}^{th}$ shot ${\varphi}_{t}$ with wavelet ($\mathrm{\Psi}$) regularization (17) (*Fig3c*):

$$mi{n}_{{\varphi}_{t}}\sum _{t=1}^{{N}_{s}}\parallel {F}_{t}C{m}_{unet}{e}^{i{\varphi}_{t}}-{d}_{t}{\parallel}_{2}^{2}+\alpha \parallel \mathrm{\Psi}{\varphi}_{t}{\parallel}_{1}$$

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 $C{e}^{i{\varphi}_{t}}$ and create virtual coils ${C}^{\ast}{e}^{-i{\varphi}_{t}}$ (

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 T_{2} and T_{2}* maps with whole-brain coverage in 12.5 sec (*Fig5*).

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msEPI diffusion acquisition at b=1000s/mm^{2 }with 0.85x0.85mm^{2} in-plane resolution using 4-shots. **(a)** Separate SENSE reconstructions for each of the R_{inplane}=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 R_{inplane}=4 with 1x1mm^{2} 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 B_{0} 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 (R_{total}=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)**.

SMS-NEATR synergistically combines machine learning and physics-based reconstruction to enable T_{2} and T_{2}* mapping with whole-brain coverage at 1x1x3mm^{3} resolution. While R_{inplane}=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.