Juyoung Lee^{1} and Jong Chul Ye^{1}

^{1}KAIST, Daejeon, Korea, Republic of

### Synopsis

Herringbone artifact is caused by power fluctuation of MR
equipment or unstable shielding. Herringbone artifact image is difficult to
analyze because it scatters on whole image region of single or multiple slices.
There is a study for MR artifact correction which can be represented as sparse
outliers on k-space. This method exploits the duality between the low-rankness
of Hankel matrix in k-space and the sparsity in the image domain. However, this
method has high computational complexity, and consumes much time. In this
research, we suggest the new effective and fast MR artifact correction method using
deep learning.

**Introduction**

There are some MR artifacts due to hardware or
software problems. Herringbone artifact, which is also called criss-cross
artifact, is caused by power fluctuation of MR equipment or unstable shielding.[1] Herringbone artifact image
is difficult to analyze because it scatters on whole image region of single or
multiple slices. There is a study for MR artifact correction which can be
represented as sparse outliers on k-space.[2] Most MR artifacts shows some sparse outliers on frequency domain, and herringbone artifact shows point-like spike noises on k-space, especially. Therefore, they exploits the duality
between the low-rankness of Hankel matrix in k-space and the sparsity in the
image domain to reduce artifact. However, this method has high computational complexity, so it consumes
much time.

Nowadays, many researchers try to apply deep neural network for MR study. Deep convolutional framelet theory[3] reveals that the deep neural network can be explained by an extension of classical signal processing theory. Inspired by this theory, we expected the deep neural network with encoder-decoder architecture also works for k-space. In this research, we suggest the new effective and fast MR artifact
correction method using k-space deep learning.

**Methods**

7T T1 weighted data are acquired from Phillips
whole body MR scanner(Phillips Achiva system) from 9 subjects with 32 channel
head coils. Acquisition parameters were as follows: TR/TE = 831/5 $$$ms$$$, 63 slices
with 0.75 $$$mm$$$ slice thickness, FOV of 220x220$$$mm^2$$$ , and 288x288 matrix size with 3/4 partial fourier
sampling. Fig.1 shows the flow and network structure of this work. The real
in-vivo data are used as labels, and random impulse noise is added on the
k-space measurement to make noisy input data. If the intensity of the impulse
is similar to the k-space signal, it is less sparse than the high intensity
case. To observe whether k-space learning method removes only impulse noise
well for different level of noise, we also used another noise data
corresponding to one third of the impulse intensity level of training data on
the inference step. Also the weighting function is applied to the input k-space
to make k-space more sparse, and the result of neural network is unweighted by
using same weighting function. Based on deep convolutional framelets theory[3]
that explains a relationship between neural network with the encoder-decoder
architecture and hankel matrix decomposition, we suggested a deep learning
method on k-space. The training network is worked on k-space domain, but
loss is
calculated in the image domain. The detailed network structure is shown in (b).
For basic module, there are 2 sets of 3x3 convolution with batch normalization
and ReLU layer(red arrow). This module is repeated 5 times with 2x2 pooling and
unpooling layers. Also, intermediate images are concatenated on decoding
parts.(blue arrow) Because k-space consists of complex values, the layer of
changing from complex to real value and the layer of changing from real to
complex value are placed at the beginning. Among 9 subjects, we used 7 subjects
for training, 1 subject data for validation, and 1 subject data for test. The
network was implemented using MatConvNet toolbox(ver.24) in MATLAB 2015a
environment (Mathwork, Natick). We used a GTX 1080 Ti graphic processor and
i7-4770 CPU (3.40GHz).**Results**

Fig.2 shows corrected image and corresponding k-space. The neural network effectively removes impulse noises on k-space. Also, herringbone artifacts on image domain are corrected clearly.(fig.3) For both
cases of impulse noise intensity level data, the proposed network shows clear
images without any noise. That is, the network is well trained to remove
impulse noise on k-space even for the low intensity impulse. It tooks only
0.0155s to 32 multi-coil and 40 slices of test subject data while the
conventional method[1] could not correct artifact due to the large data size.**Conclusion**

This work shows the novel MR artifact correction
method using deep learning method. The proposed method shows good performance
to remove impulse noises on k-space and noise on image domain. We expect that this method becomes to apply other MR artifact
research.### Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT (NRF-2016R1A2B3008104)

### References

1. A.Stadler
et al, European radiology, 17.5 (2007) 2. K.H.Jin et al, Magn Reson Med 78
(2017) 3. J.C.Ye et al, Siam J Imaging Sci 11.2 (2018)