Motion-aligned 4D-MRI reconstruction using higher degree total variation and locally low-rank regularization

Four-dimensional magnetic resonance imaging (4D-MRI) is becoming increasingly important in radiotherapy treatment planning for its ability to simultaneously provide 3D structural information and temporal profiles of the examined tissues in a non-ionizing manner. However, the relatively long acquisition time and the resulting motion artifacts severely limit the further application of 4D-MRI. In this paper, we propose a novel motion -aligned reconstruction method based on higher degree total variation and locally low-rank regularization (maHDTV-LLR) to recover 4D MR images from the highly undersampled Fourier coefficients. Specifically, we propose a two-stage reconstruction framework alternating between a motion alignment step and a regularized optimization reconstruction step. Moreover, we incorporate the 3D-HDTV and the locally low-rank penalties into a unified framework to simultaneously exploit the spatial and temporal correlation of the 4D-MRI data. A fast alternating minimization algorithm based on variable splitting is utilized to solve the optimization problem efficiently. The performance of the proposed method is demonstrated in the context of 4D cardiac and abdominal MR images reconstruction with high undersampling factors. Numerical results show that the proposed method enables accelerated 4D-MRI with improved image quality and reduced artifacts.