Yuhsuan Wu^{1}, Erpeng Dai^{1}, Chun Yuan^{1,2}, and Hua Guo^{1}

In this work, we preliminarily demonstrate the deep-learning-based reconstruction can be used for under-sampled diffusion imaging. By integrating the sharable information from multiple diffusion directions, the under-sampled data can be nicely recovered.

Purpose

Scan speed is a critical issue in MRI. Partially parallel acquisition (PPA) can be used to accelerate the acquisition of k-space and thus save imaging time. Currently, there are many PPA reconstruction methods based on information redundancy in phase coil arrays, such as SENSE and GRAPPAAcquisition In vivo brain data were acquired on a Philips 3.0T Achieva TX
MRI scanner (Philips Healthcare, Best, The Netherlands) using a 32-channel head
coil. Three volunteers were included in this study. A 4-shot interleaved EPI
(iEPI) sequence with a 2D navigator was used^{(7)}. Diffusion
encoding was applied along 32 directions with b=800 s/mm2. The diffusion
encoding directions were uniformly distributed on a hemisphere [HG1] in q-space. The
main imaging parameters were: FOV=207×207×96 mm3, voxel
size=1.2×1.2 mm2, slice thickness=4 mm, no partial Fourier, TE=86 ms, TR=4.2 s.
GRAPPA with a compact kernel (GRAPPA-CK)^{(8)} was used
to correct inter-shot phase variations and reconstruct the image of each shot
and channel. After that, the images were combined to generate the final DW
images, which were used as references.

Simulation and preprocessing The reconstructed image of each shot and channel were
complex averaged along the shot dimension to remove the phase errors among
different shots. The newly generated image of each channel were Fourier
transformed to k-space and manually 2-fold under-sampled. Note that this
actually simulate the accelerated acquisition of single shot EPI (ssEPI).
4-shot iEPI was used in the acquisition mainly for SNR and geometric distortion
consideration.
To compare with the
traditional acceleration in multi-shot EPI, 2 out of 4 shots was extracted from
the originally acquired data. Then the same GRAPPA-CK reconstruction procedure
was conducted^{(8)}.

Deep learning framework In this deep learning
model, we need to solve the aliasing artifacts as well as recover the missing
data from different diffusion directions. We proposed a model based on
Generative Adversarial Networks (GAN)^{(6)}. GAN includes two parts, which are generator network G and
discriminator network D. In generator network, we used U-net as the model. The
framework is shown in Fig.2. Vgg 16 was used for calculating content loss. It
can make image more realistic. We used two sets of diffusion-weighted images as
training data while the other set of diffusion-weighted images as testing data.

Loss function Before k-space sharing layers, the outputs of U-net should be similar with the reference images. Thus, we minimized the loss between outputs after U-net and reference images, which is L_middle. After a few of epochs, we minimized the total loss which can be written as:

$$L_{total}=α\cdot{L_{middle}}+β\cdot{L_{image}}+L_{D}+γ\cdot{L_{feature}}$$

L_{middle} is the loss between reference images and outputs of U-net. L_{image }is the loss between reference images and outputs of k-space sharing layers. L_{feature }is the content loss.

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Fig 1. We filled missing data from the direction which is close to the targeted directions. If direction 2 is closest to direction 1, we use the data colored in red to fill the blank space in direction 1. The result is combined data.

Fig 2 .The framework of the deep learning model. a, Generator network contains two parts. One is U-net while the other is k-space sharing. In U-net. Black is convolution layer. Red is combining two convolution output. Blue is pooling layer. b, Discriminator network contains two parts. One is content loss while the other is discriminator loss. content loss is calculated by the outputs of third convolution layer.

Fig 3. The upper row is undersampled data from acquisition directly. The lower row is undersampled data from simulation. In simulation, we didn't consider motion-induced phase errors. Thus, the aliasing in upper low is twice aliasing than lower in both 2-skip undersampled data and combined image.

Fig 4. The upper row is reconstruction image of undersampled data from acquisition directly. The lower row is reconstruction image of undersampled data from simulation. We compared them with the GRAPPA-based method. In our proposed method, the SNR is better than GRAPPA-based method. However, the results of our output are blurring.