A motion assessment method for reference stack selection in fetal brain MRI reconstruction based on tensor rank approximation

Slice-to-volume registration and super-resolution reconstruction are 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 among all input stacks as a reference for registration. An accurate and unbiased motion assessment (MA) is thus crucial for successful selection. Here, we presented an 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. Experiments on linearly and randomly simulated motion illustrated that CP demonstrated higher sensitivity in detecting small motion with a lower baseline bias, and achieved a higher assessment accuracy of 95.45% in identifying the minimum motion stack, compared to the SVD-based method with 58.18%. CP also showed superior motion assessment capabilities in real-data evaluations. Additionally, combining CP with the existing SRR-SVR pipeline significantly improved 3D volume reconstruction. The results indicated that our proposed CP showed superior performance compared to SVD-based methods with higher sensitivity to motion, assessment accuracy, and lower baseline bias, and can be used as a prior step to improve fetal brain reconstruction.