Kinam Kwon^{1}, Jaejin Cho^{1}, Seohee So^{1}, Byungjai Kim^{1}, Namho Jeong^{1}, and HyunWook Park^{1}

Metallic implants induce large field perturbations, which generate various types of artifacts according to the spatial encoding mechanisms in MRI. Especially, a frequency encoding dimension is influenced by bulk displacements with off-resonance frequencies and the pixel sizes are distorted in the frequency encoding dimension. In the abstract, a new learning-based method is proposed to map two metal-induced-artifacts images with positive and negative-polarity readout gradients into a metal-induced-artifacts-free image. Simulated data was utilized for training the network instead of real MR data that requires many resources to be collected.

The proposed network was modified from U-net as shown in figure 1.^{4}
The convolutional layers are appropriate to consider the bandlimited property
of the field perturbation induced by metal. A multi-scale architecture of U-Net
is efficient to increase receptive fields. The skip connection of each level
(yellow) is utilized to avoid loss of information. The skip connection between
input and output (gray) is utilized to learn only residual values between the
connection, which helps learning to be stable and fast.^{5} Sub-images
with 108$$$\times$$$108 and the
corresponding sub-image with 66$$$\times$$$66 are
utilized for input and output in the proposed network, respectively.

The overall scheme to generate the training data for the proposed
network is displayed in figure 2. We additionally generate susceptibility maps
by randomly performing erosion, dilation, and rotation operations and changing
susceptibility values from the digital model of total hip replacement implant.^{6}
The field maps are computed from the generated susceptibility maps.^{7}
Two images with positive and negative-polarity readout gradients ($$$I_{RO+}$$$ and $$$I_{RO-}$$$) are
generated, respectively, as follows:

$$I_{RO+}(x,y,b)=\rho(x+\frac{f-f_{b}}{rBW},y)\cdot RF(f-f_{b}) [1]$$

$$I_{RO-}(x,y,b)=\rho(x-\frac{f-f_{b}}{rBW},y)\cdot RF(f-f_{b}) [2]$$

where $$$x$$$ and $$$y$$$ are indices to represent spatial dimensions along the readout direction and the phase encoding direction, respectively, and $$$b$$$ is the spectral bins. In eqs. [1] and [2], $$$f$$$, $$$f_{b}$$$, and $$$rBW$$$ are off-resonance frequency, center frequency of the bin, and readout bandwidth per pixel, respectively; $$$\rho$$$ is the original image without spatial distortion; $$$RF$$$ is a function representing the RF excitation profile. A corresponding artifact-free image is generated as follows:

$$I_{RO-free}(x,y,b)=\rho(x,y)\cdot RF(f-f_{b}) [3]$$

In the abstract, natural images from ImageNet
dataset were utilized for the original images.^{8} Total 0.5 million
training data were generated by variations of field maps and RF profiles, and various
original images.

To show the performance of the proposed method, a physical phantom
experiment was conducted using the 3T MRI system (Siemens Verio, Germany). The
imaging sequences were based on MAVRIC,^{9} and a physical phantom with
total hip replacement implant was scanned twice using positive and
negative-polarity readout gradients. Their imaging parameters are given as
follows: TR/TE=800/5ms, the number of spectral bins=25 (Gaussian RF profiles with
2.25 full-width-half-maximum separated by 1kHz), matrix size=512$$$\times$$$160$$$\times$$$20, voxel
size=1$$$\times$$$1$$$\times$$$5$$$mm^{3}$$$, and readout
bandwidth=780Hz/pixel.

Results

We proposed a U-net based network to map two images with positive and negative-polarity readout gradients into artifact-free image. The simulated data was utilized for learning the network to overcome an impractical work that collects pairs of images with and without metal-induced artifacts. The proposed method significantly reduced the imaging time to acquire metal-artifact-free images by using the positive and negative-polarity readout gradients instead of all phase encodings.

The proposed network was learned by minimizing mean squared error
(MSE) between the estimated outputs and desired outputs. The MSE loss function
has been known to produce blurring in estimated results,^{10} and their
effects can be seen in figures 3 and 4 (blue arrows). Various loss functions
like gradient difference loss would be applied to relieve this problem in
future works.

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2. Koch KM, et al. Imaging Near Metal: The Impact of Extreme Static Local Field Gradients on Frequency Encoding Processes. MRM 2014;71:2024-2034.

3. Artz NS, et al. Spectrally Resolved Fully Phase-Encoded Three-Dimensional Fast Spin-Echo Imaging. MRM 2014;71-681-690.

4. Ronneberger O, et al. U-Net: Convolutional Networks for Biomedical Image Segmentation. MICCAI 2015:234-241.

5. He K, et al. Deep Residual Learning for Image Recognition. CVPR 2016.

6. Shi X, et al. Metallic Implant Geometry and Susceptibility Estimation Using Multispectral B0 Field Maps. MRM 2017;77:2402-2413.

7. Marques JP, et al. Application of a Fourier-Based Method for Rapid Calculation of Field Inhomogeneity Due to Spatial Variation of Magnetic Susceptibility. Concepts in Magnetic Resonance Part B: Magnetic Resonance Engineering 2005;25:65-78.

8. Russkovsky O, et al. ImageNet Large Scale Visual Recognition Challenge. IJCV, 2015

9. Koch KM, et al. A Multispectral Three-Dimensional Acquisition Technique for Imaging Near Metal Implants. MRM 2009;61:381-390.

10. Mathieu M, et al. Deep Multi-Scale Video Prediction beyond Mean Square Error. ICLR 2016.