Doohyun Park^{1}, Taejoon Eo^{1}, Taeseong Kim^{1}, Jinseong Jang^{1}, and Dosik Hwang^{1}

^{1}Yonsei University, Seoul, Republic of Korea

### Synopsis

The purpose of this study is
to eliminate the aliasing artifacts in accerelated radial MRI. We designed a Cross-Domain
deep-learning network, called SISI-Net(Sinogram-Image-Sinogram-Image
Network). This is
an architecture to gradually solves data sparsity problems by iteratively
learning the radial sampling data in the sinogram domain and the reconstructed
data in the image domain. As a result, proposed network could remove
aliasing artifacts effectively while maintaining structural information.

Introduction

Shortening MR acquisition time is one of the
important areas of MR researches. To achive higher speed,
various reconstruction methods have been developed for undersampled data. In
particular, deep-learning based methods have recently been spotlighted,
especially, iterative deep-learning is also being researched.^{1} Also, deep-learning
can be efficiently performed on the sinogram domain obtained by 1D inverse
fourier transform of radial k-space as well as the image domain.^{2} In this
regard, we propose an iterative cross-domain CNN method that learns sinogram
and image iteratively.

### Methods

Radial MR can be used as a very effective
acceleration method when combined with deep learning method. It is because that
undersampled radial MR data can be efficiently interpolated in the sinogram
domain through radon and iradon transform and is well trained for artifact
removal through a deep-learning structure. To make training data set, we need complex process as in
fig 1. First, the 2D-Fourier transform of the image is performed and then the
512 spokes radial data is generated by inverse gridding. Here, because it is
common to use oversampling factor 2, 512 spoke is applied.^{3} Second, MR sinogram
data were generated by 1D inverse fourier transform according to each spokes. Third,
1/8 undersampled 64 spokes radial MR data is interpolated through radon and
iradon transform operations.
Fig. 2 shows the architecture we have developed. It consists of two steps:
first step is sinogram domain CNN (SCNN), which learns on the sinogram. Although
SCNN is insufficient for artifact removal, but it uses raw data, so it has a
characteristic that information loss is minimized. Second step is image domain
CNN (ICNN), which learns on the image. This is specialized for artifact
removal, but there is a disadvantage that the output image is blurred. Each CNN output of the cross-domain structure is uesd by
the input of next CNN. We maximized performance by iteratively repeating the fig.
2 structure twice.
We used 457 T2 fluid attenuated inversion recovery brain images(size=256*256) from Alzheimer’s Disease Neuroimaging
Initiative MRI data.^{4} 450 images were used for the train data, and 7 images were
used for the test data. In each CNN layer, the ReLU transfer function is used
to transfer the weight even at low gradient values, so that the fine learning
can be performed as the learning in the SISI-Net structure becomes saturated.
Patch size was 32*32, convolution filter size was 3*3, and the number of filter
was 64.### Results

We
compared our SISI-Net result with I-Net, KIKI-Net, R6_BM3D-mri, Wang’s methods.^{5, 6} In fig. 3, Reference image (a), undersampled radial MR image (b), I-Net (c), KIKI-Net (d), SISI-Net, our result (e), each magnified images (f-j) are
shown. In both first and third row images, I-Net
result has artifacts and cannot correct sufficiently. In image row 1, streak
artifacts that did not exist in reference image (a), can be seen in KIKI-Net
result (d) but not in SISI-Net result (e). This means that aliasing artifacts
in the undersampled image (b) are misinterpreted as truly exists structures in
KIKI-Net. In image row 3, we can see that the actual image structure is restored
well in the SISI-Net result (e), but not in the KIKI-Net result (d). This can
be interpreted that learning in the sinogram domain shares structural information
with neighboring pixels in the convolution process, but k-space learning is
not. In fig. 4, Reference image (a), undersampled radial MR
image (b), R6-BM3D-mri method (c), Wang’s method (d), SISI-Net, our result (e), each
magnified images (f-j) are shown. BM3D method shows removed streak artifact
image but too much blurred. Wang’s method shows similar with I-Net result. Each average PSNR of 7 test images are (Underampled = 28.60, I-Net =
35.41, KIKI-Net = 36.58, R6_BM3D = 38.26, Wang’s = 32.50, SISI-Net = 39.40)### Conclusion

We have developed a iterative deep learning
architecture that improves image quality with only a few spokes radial MR data.
In addition, it was confirmed that the result image is improved by repeatedly
performing the sinogram domain and the image domain which is the reconstruction
of the sinogram. The repetitive learning structure using sinogram can be used
not only for radial MR but also for sparse-view undersampling of CT.### Acknowledgements

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.2016R1A2B4015016).### References

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