Dynamic MR Image Reconstruction From Highly Undersampled (k, t)-Space Data Exploiting Low Tensor Train Rank and Sparse Prior

Abstract

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. INDEX TERMS Dynamic MR imaging, tensor train, sparsity, the alternating direction multiplier method.

Recovering low‐rank tensor from limited coefficients in any ortho‐normal basis using tensor‐singular value decomposition

“…The state-of-the-art CS d-MRI methods including L1-TV [44], k-t SLR [20], RPCA-DMRI [45], TuckerDMRI [19] and PS-L1 [23] etc. We have conducted various comparisons of k-t tSVDTV (the t-SVD method combined with sparsity), k-t SLR, RPCA-DMRI, L1-TV, and TuckerDMRI methods in our previous papers [21,25]. Zero-filled method fills zeros into the undersampled k-space, then gets the reconstructed image…”

“…We can see that Tucker method is comparable to t-SVD method when all the sampling mask of the frontal slices are the same. More numerical results related with the t-SVD method can be found in our previous papers [21,22,25].…”

“…In recent years, we have tried to use different tensor decomposition frameworks in sparse sampling MRI. In our previous work [21], the TT decomposition framework is used to improve the quality of dynamic MR image reconstruction under sparse sampling. In ref.…”

“…In some applications such as synthetic aperture radar (SAR) imaging [17,18], dynamic magnetic resonance imaging (d-MRI) [19,20], a limited number of measurements, which are expansion coefficients with respect to some basis, are obtained to reconstruct the original images. For example, sparse sampling in MRI can accelerate imaging speed significantly [16,[21][22][23][24][25]. In recent years, we have tried to use different tensor decomposition frameworks in sparse sampling MRI.…”

Accelerated dynamic MR imaging with joint balanced low‐rank tensor and sparsity constraints

“…This highly unbalanced matricization scheme (i.e., the number of rows is much smaller than the number of columns) determines that the Tucker rank cannot describe the global information of the tensor. 25,29,30 Recently, the tensor train (TT) rank 31,32 defined based on the well-balanced matricization scheme has been proposed and applied to the tensor completion problem. 29,33 In this paper,we explore the low-rank property of DMR data from the perspective of the balance of unfolding ways by introducing the TT rank.…”