  Purpose: Slice-to-volume registration and super-resolution reconstruction
(SVR-SRR) is commonly used to generate 3D volumes of the fetal brain from 2D
stacks of slices acquired in multiple orientations. A critical initial step in
this pipeline is to select one stack with the minimum motion as a reference for
registration. An accurate and unbiased motion assessment (MA) is thus crucial
for successful selection. Methods: We presented a MA method that determines the
minimum motion stack based on 3D low-rank approximation using CANDECOMP/PARAFAC
(CP) decomposition. Compared to the current 2D singular value decomposition
(SVD) based method that requires flattening stacks into matrices to obtain
ranks, in which the spatial information is lost, the CP-based method can
factorize 3D stack into low-rank and sparse components in a computationally
efficient manner. The difference between the original stack and its low-rank
approximation was proposed as the motion indicator. Results: Compared to
SVD-based methods, our proposed CP-based MA demonstrated higher sensitivity in
detecting small motion with a lower baseline bias. Experiments on randomly
simulated motion illustrated that the proposed CP method achieved a higher
success rate of 95.45% in identifying the minimum motion stack, compared to
SVD-based method with a success rate of 58.18%. We further demonstrated that
combining CP-based MA with existing SRR-SVR pipeline significantly improved 3D
volume reconstruction. Conclusion: The proposed CP-based MA method showed
superior performance compared to SVD-based methods with higher sensitivity to
motion, success rate, and lower baseline bias, and can be used as a prior step
to improve fetal brain reconstruction.
