Chang-Le Chen^{1}, Yu-Jen Chen^{2}, Yung-Chin Hsu^{2}, and Wen-Yih Isaac Tseng^{1,2,3}

Unexpected phase errors occurred in the k-space of the diffusion spectrum EPI sequence would lead to abrupt shifts in the phase-encoding direction across different diffusion gradient directions which cause shaking artifact of the image. The shaking artifact can lead to errors in image registration and diffusion index calculation. Here, we developed an estimated maximum likelihood method to detect and correct image shifts. After correcting the shaking artifact, the performance of registration and the diffusion index calculation were significantly improved comparing to the images without correction.

1. Wedeen VJ, et al. "Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging." Magn Reson Med 54 (2005): 1377–1386.

2. Myung, In Jae. "Tutorial on maximum likelihood estimation." Journal of mathematical Psychology 47.1 (2003): 90-100.

3. Chen, Yu-Jen, et al. "Automatic whole brain tract-based analysis using predefined tracts in a diffusion spectrum imaging template and an accurate registration strategy."Human brain mapping 36.9 (2015): 3441-3458.

4. Gouttard S, et al. "Measures for validation of DTI tractography." Proc Soc Photo Opt Instrum Eng (2012): 8314:83140J.

Figure 1: Illustration
of the shaking artifact. Images translate along the phase-encoding direction
across different directions of diffusion gradients, possibly due to unexpected
errors in image reconstruction during DSI scanning. When viewing images sequentially, it appears
like shaking motion of the head.

Figure 2: Shaking
artifact causes misalignment of images, leading to erroneous diffusion index calculation. In the generalized fractional anisotropy (GFA)
map, the errors in
diffusion index calculation produce a bright margin around the map. Correlation coefficients between the white
matter (WM) tissue probability map (TPM) from T1-weighted images and the GFA
map from DSI were measured to assess the performance of image registration. A
higher correlation coefficient between the WM TPM and GFA maps indicates better
registration than the one with a lower correlation coefficient.

Figure 3: Procedures
of correcting shaking artifact. Images went through a series of image processing
including normalization, pre-masking, denoising, sharpening and binarization to
obtain the binary mask. In the estimated maximum likelihood process, the mask
was used as a variable in likelihood function, and the estimated image shifts were
determined by seeking the probable image shift P (P could be positive (p^{+}),
negative (p^{-}) or no (p^{0}) shift) that maximized the
function. The estimated P was used to reconstruct the corrected image, I_{C}.

Figure 4: In the
simulation study, SA in the simulation group was eliminated after correction.
The performance of image registration, as assessed by the correlation
coefficient between WM TPM and GFA maps, in the correction group was better
than that in the simulation group. In the in-vivo study, real SA was removed after
applying correction algorithm. The results showed that image registration was
improved, and so the deviation of the diffusion index was reduced, as indicated
by the disappearance of the abnormal boundary in GFA map.

Equation 1: The maximum likelihood function, where argmax stood
for argument of the maximum, I_{R} was the reference image, I_{D}
was the image with shift, D was different diffusion encoding directions, and P
was the probable image shift. Once the I_{D} with the estimated P
satisfied the maximum of likelihood function of I_{R}, the estimated
image shift was used to reconstruct the corrected image, I_{C}.