Qianqian Zhang^{1}, Guohui Ruan^{1}, Wei Yang^{1}, Kaixuan Zhao^{1}, Ed X. Wu^{2,3}, and Yanqiu Feng^{1}

The Gibbs-ringing artifact is caused by the insufficient sampling of the high frequency data. Existing methods generally exploit smooth constraints to reduce intensity oscillations near high-contrast boundaries but at the cost of blurring details. This work presents a convolutional neural network (CNN) method that maps ringing images to their ringing-free counterparts for Gibbs-ringing artifact removal in MRI. The experimental results demonstrate that the proposed method can effectively remove Gibbs-ringing without introducing noticeable blurring.

**Purpose**

**Introduction**

Gibbs-ringing artifact refers to a
series of spurious intensity oscillations near sharp edges in MR images.^{1} This artifact is
caused by the insufficient sampling of high-frequency data in the k-space
domain. In practice, the ringing artifact degrades image quality, and can
complicate diagnosis and affect the subsequent parameter quantification.^{2,3
}To tackle this problem, model-based data extrapolation or image smoothing
approaches have been developed, and they can reduce this artifact but at the
expense of blurring.^{4,5}

Machine learning methods such as autoregressive modeling and
multilayer neural network have been trained on known truncated data set and
then used to predict unknown high frequency components from the measured low
frequency data.^{6-8} Motivated
by the CNN for compression artifact reduction,^{9 }this work aims to develop a CNN-based
method for Gibbs-ringing artifact reduction in MRI.

**Methods**

Our proposed method employs a CNN that
directly learns an end-to-end mapping from a ringing image to a ringing-free
image, and then obtain the final output by replacing the low-frequency part of
the CNN-estimated image with the measured k-spaced data. We name the proposed
method as Gibbs-ringing artifact reduction using CNN (GRA-CNN). The overall architecture of
GRA-CNN is shown in Figure 1. GRA-CNN consisted of a four-layer convolutional
network. Rectified linear units (ReLU, max(0,x))^{10} was applied as the activation function, and batch
normalization^{11} was used to accelerate network training and boost
accuracy. The filter size was set f_{1}
= 9, f_{2} = 7, f_{3} = 1, and f_{4} = 5; and the filter number
was set n_{1} = 64, n_{2} = 32, n_{3} = 16 and n_{4}
= 1. The network parameters Θ = {Wi,
bi, i = 1,2,3,4} were learned for the
end-to-end mapping function. The mean-squared error (MSE) was used as the loss function
and minimized by using stochastic gradient descent with the standard
backpropagation.

The training data consisted of 17532 T2-weighted (T2W) brain images of 136 healthy adult subjects from
the human connectome project (http://www.humanconnectome.org, 900 Subjects Data). Testing
data consisted of T2W and
diffusion-weighted (DW) images. The T2W images of normal brain were
acquired on a 1.5T MR scanner (OPTIMA MR360, GE, America) using the fast-spin-echo
sequence: TR/TE=5900/117 ms, FOV=24×24 cm^{2}, pixel size=0.47×0.47 mm^{2},
and slice thickness=6.0 mm. The brain tumor were acquired on a 3T scanner
(Achieva, Philips, Netherlands) using the fast-spin-echo sequence: TR/TE = 3000/80
ms, FOV=22×22 cm^{2}, pixel size=0.43×0.43 mm^{2}, and slice thickness=6.0
mm. The DW data was acquired on a 3T scanner (Achieva, Philips, Netherlands)
using an interleaved EPI sequence: TR/TE=3000/83 ms, FOV=22×22 cm^{2},
pixel size=1.0×1.0 mm^{2},
slice thickness=6.0 mm, shots=6, and b-value=800
s/mm^{2}, and diffusion directions=10.

We implemented the GRA-CNN network using the MatConvNet package [46]. In the training, the convolution parameters were randomly initialized from a Gaussian distribution with a standard deviation of 0.001, and the learning rate was set 10-4. The root-mean-square error (RMSE), peak signal-to-noise ratio (PSNR) and structure similarity (SSIM) index were calculated for the quantitative evaluation.

**Results**

Figure 2 presents the results of Gibbs-ringing reduction on a representative T2W normal brain images with 50% data truncation in one dimension and both dimensions. The low-pass hamming filter removes the ringing artifact, but shows a smoothing of rapidly changing details and reduces PSNR. In contrast, GRA-CNN effectively eliminates the ringing artifact without noticeable blurring.

The application of the proposed method on the T2W images of brain tumor is presented in Figure 3. The GRA-CNN model trained by using normal brain images also successfully removes ringing artifact in brain tumors, without noticeable blurring.

Figure 4 shows the application of the proposed method to DW images. The ringing artifacts are successfully removed from DW images. The mean diffusivity (MD) map is significantly improved by the proposed method, and the fractional anisotropy (FA) maps before and after artifact suppression are comparable.

Table 1 presents the quantitative evaluation of the proposed method. The GRA-CNN method consistently generates images with improved RMSE, PSNR and SSIM values, for both T2- and diffusion-weighted images.

**Discussion & Conclusion**

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- Veraart, J., et al., Gibbs ringing in diffusion MRI. Magn Reson Med, 2015.
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- Constable, R.T. and R.M. Henkelman, Data extrapolation for truncation artifact removal. Magn Reson Med, 1991. 17(1): p. 108-18.
- Smith, M.R., et al., Application of autoregressive modelling in magnetic resonance imaging to remove noise and truncation artifacts. Magn Reson Imaging, 1986. 4(3): p. 257-61.
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- Yan, H. and J. Mao, Data truncation artifact reduction in MR imaging using a multilayer neural network. IEEE Trans Med Imaging, 1993. 12(1): p. 73-7.
- Dong, C., et al. Compression artifacts reduction by a deep convolutional network. in Proceedings of the IEEE International Conference on Computer Vision. 2015.
- Nair, V. and G.E. Hinton. Rectified linear units improve restricted boltzmann machines. in Proceedings of the 27th international conference on machine learning (ICML-10). 2010.
- Ioffe, S. and C. Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. in International Conference on Machine Learning. 2015.

Figure
1. the framework of the proposed method

Figure
2. the 1D and 2D results of T2-weighted image

Figure
3. the 1D results of tumor
T2-weighted image

Figure
4. the 1D results of diffusion-weighted image, MD and FA map was calculated by pre-average

Table
1. Quantitative evaluation of the proposed method in terms of the
root-mean-square error (RMSE), peak signal-to-noise ratio (PSNR) and structure
similarity (SSIM) index