Dynamic MR image reconstruction from highly undersampled (k, t)-space data exploiting low tensor train rank and sparse prior

Dynamic magnetic resonance imaging (dynamic MRI) is used to visualize living tissues and their changes over time. In this paper, we propose a new tensor-based dynamic MRI approach for reconstruction from highly undersampled (k, $t$ )-space data, which combines low tensor train rankness and temporal sparsity constraints. Considering tensor train (TT) decomposition has superior performance in dealing with high-dimensional tensors, we introduce TT decomposition and utilize the low rankness of TT matrices to exploit the inner structural prior information of dynamic MRI data. First, ket augmentation (KA) scheme is used to permute the 3-order (k, $t$ )-space data to a high order tensor and low rankness of each TT matrix is enforced with different weights. To reduce the computational complexity, we replace the nuclear norm of TT matrices with the minimum Frobenius norm of two factorization matrices to avoid singular value decomposition. Secondly, the $l_{1}$ norm of the Fourier coefficients along the temporal dimension is added as a sparsity constraint to further improve the reconstruction. Lastly, an effective algorithm based on the alternating direction method of multipliers (ADMM) is developed to solve the proposed optimization problem. Numerous experiments have been conducted on three dynamic MRI data sets to estimate the performance of our proposed method. The experimental results and comparisons with several state-of-the-art imaging methods demonstrate the superior performance of the proposed method.