Neha Koonjoo^{1,2,3}, Bo Zhu^{1,2,3}, Matthew Christensen^{1,2}, John E. Kirsch^{1,2}, Bragi Sveinsson^{1,2,3}, and Matthew S Rosen^{1,2,3}

Low intrinsic Signal-to-Noise
Ratio (SNR) in diffusion-weighted (DW) images are recurrent issues especially
at high b-values.
Here, we apply the deep
neural network image reconstruction technique, AUTOMAP (Automated Transform by
Manifold Approximation) to *in-vivo* diffusion-weighted MR data acquired at 1.5 T
with varying b-values. In addition, apparent diffusion coefficient (ADC) maps were
assessed. We also compared the reconstruction of the images using two different
training corpura. The results for
AUTOMAP reconstruction showed a significant increase in SNR.

Introduction

Long scan times and low intrinsic Signal-to-Noise Ratio (SNR) in diffusion-weighted (DW) images are recurrent issues especially at high b-values (b>1000 s/mm
Training set: Two training **corpora**
were assembled 1) from 61,000 2D diffusion-weighted (DW) brain MR images which included b-values ranging from 1000 – 10000s/mm^{2} and 2) from 51,000
2D T_{1}-weighted (T1-W) brain MR images. Both training corpora were selected
from the MGH-USC Human Connectome Project (HCP)^{4} public database. The images were cropped to
256 × 256 and were subsampled to 128×128, symmetrically tiled to create translational invariance and finally
normalized to the maximum intensity of the data. To produce the corresponding k-space representations for training,
each image was Fourier Transformed with MATLAB’s native 2D FFT function.

Architecture of NN: The NN was trained
to learn an optimal feed-forward reconstruction of k-space domain into the image domain. The real and the imaginary
part of datasets were trained separately. The network, described in Figure 1,
was composed of 2 fully connected layers (input layer and 1 hidden layer) of
dimension n^{2}×1 and activated by the hyperbolic tangent function.
The 3rd layer was reshaped to n × n for convolutional processing.
One convolutional layer, C1 convolved 64 filters of 5×5 with stride 1
followed by a rectifier nonlinearity. The final output layer deconvolves the C1
layer with 64 filters of 7×7 with stride 1. The output layer resulted into
either the reconstructed real or imaginary component of the image.

Data Acquisition & Reconstruction: 2D in vivo DW brain images at 1.5 T were
acquired with single shot Spin Echo EPI sequence. The sequence parameters were:
TR =5000ms, TE = 136ms, TI = 2500ms, matrix size = 128×128, spatial resolution = 1.8mm×1.8mm, a slice thickness = 6.5 mm, number
of slices = 24, number of coils = 4 and number of averages (NA) was set to 1.
Images were acquired with b-values: 0, 200, 500, 800, 1000, 1300, 1500, 2000,
2500, 3000 s/mm^{2} and the diffusion gradients were along 3 directions.
For AUTOMAP reconstruction, 1 image slice from each coil, each b-value and each
direction were Fourier Transformed with MATLAB’s native 2D FFT function and
reconstructed using either trained brain models above.

Data Analysis: The signal
magnitude of the AUTOMAP reconstructed images were normalized to the scale of
the conventional IFFT reconstructions with a constant scalar determined by
matching the AUTOMAP and IFFT intensities of the ventricles at b-value=0. SNR
was then computed by dividing the signal magnitude by the standard deviation of
the noise. The gain in SNR was also calculated by taking the ratios of SNRs of
the AUTOMAP reconstructed images over the IFFT reconstructed images. The
apparent diffusion coefficient (ADC) maps were also computed with , where , is the signal intensity with the
gradient factor b-value=1000 s/mm^{2} and , the signal intensity with all
diffusion-sensitizing gradients turned off.

**Discussion & Conclusion**

The reconstruction performance of AUTOMAP on low SNR data demonstrates the robustness of the reconstruction technique and its high immunity to noise in the ULF regime. Due to lack of correct diffusion coefficient metrics, the quantitative assessment of the ADC maps was not conducted. Future work will include the application of AUTOMAP on real raw in vivo data diffusion weighted datasets without corrections and a deeper assessment on the parametric ADC maps.

1.Haldar, Justin P et al. “Improved diffusion imaging through SNR-enhancing joint reconstruction” Magnetic resonance in medicine vol. 69,1 (2012): 277-89.

2. F. Lam, S. D. Babacan, J. P. Haldar, N. Schuff and Z. Liang, "Denoising diffusion-weighted MR magnitude image sequences using low rank and edge constraints," 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), Barcelona, 2012, pp. 1401-1404

3.‘Image reconstruction by domain transform manifold learning’, B. Zhu and J. Z. Liu and S. F. Cauley and B. R. Rosen and M. S. Rosen, Nature 555 487 EP - (2018).

4 ‘MGH–USC Human Connectome Project datasets with ultra-high b-value diffusion MRI’, Fan, Q. et al. NeuroImage 124, 1108–1114 (2016).

Figure 1:
Description of neural network: a) An optimal one-to-one mapping of the sensor
domain (here k-space) onto the image domain using supervised learning. The
training process learns a robust low-dimensional joint manifold 𝒳×𝒴
conditioned by the reconstruction function 𝑓(𝑥)
= 𝜙f ∘𝑔∘𝜙𝑥-1(𝑥);
b) AUTOMAP is implemented with a deep neural network architecture composed of 3
fully-connected layers (FC1 to FC3) with hyperbolic tangent activations
followed by a convolutional autoencoder (FC3 to Image) with rectifier
nonlinearity activation (figure adapted from Ref 1).

Figure 2:
Performance of AUTOMAP on *in-vivo* diffusion-weighted images using two training
sets– A) model trained on diffusion weighted brain images and B) model trained
on T_{1}-weighted brain images. C) *In-vivo* reconstruction with IFFT.
(Left-to-right) – The reconstruction was assessed across different b-values
ranging from 0 to 1000 s/mm^{2}. All the images are normalized as
described in Methods, and the window level is the same for each b-value.

Figure 3:
Performance of AUTOMAP on in vivo diffusion-weighted images with high b-values
using two training sets– A) model trained on diffusion weighted brain images
and B) model trained on T_{1}-weighted brain images. C) In vivo reconstruction
with IFFT. (Left-to-right) – The reconstruction was assessed across different
b-values ranging from 1300 to 3000 s/mm^{2}. All the images are
normalized as described in Methods, and the window level is the same for each
b-value.

Figure 4: Signal-to-Noise
Ratio of reconstructed data. Plotted on the left is SNR for each reconstructed
method (black – AUTOMAP based on the DW trained model, blue – AUTOMAP based on
the T1-W trained model and red - IFFT) as a function of the b-values. Right is
the ratio of SNR for AUTOMAP to SNR for IFFT. This is a measure of
reconstruction performance of AUTOMAP over IFFT as a function of the b-values.

Figure 5: ADC
maps of the reconstructed data – A is the ADC map computed from the IFFT
diffusion images; B is the ADC map computed from AUTOMAP using a training set
composed of diffusion-weighted brain images and C is the ADC map computed from
AUTOMAP using a training set composed of T_{1}-weighted brain images. All the maps
are windowed to the same level and the units for the ADC maps is mm^{2}/s.