Accelerating Dynamic MRI Reconstruction Using Adaptive Sequentially Truncated Higher-Order Singular Value Decomposition.

BACKGROUND: Dynamic magnetic resonance imaging (dMRI) plays an important role in cardiac perfusion and functional clinical exams. However, further applications are limited by the speed of data acquisition. OBJECTIVE: A low-rank plus sparse decomposition approach is often introduced for reconstructing dynamic magnetic resonance imaging (dMRI) from highly under-sampling K-space data. In this paper, the reconstruction problem of DMR is transformed into a low-rank tensor plus sparse tensor recovery problem. METHODS: A sequentially truncated higher-order singular value decomposition method is proposed to quickly approximate the low-rank tensor space structure and learn sparse components by adding a tensor kernel norm to the low-rank tensor and a l1 norm to the sparse tensor to constrain the two parts at the same time. The optimization problem is solved by using the iterative soft-thresholding algorithm; therefore, under the premise of ensuring the accuracy of the data, the amount of computation can be effectively reduced. RESULTS: Compared with the state-of-the-art methods, the experimental results show that the proposed method can achieve better performance in terms of reconstruction speed and reconstruction quality on 3D and 4D dMRI datasets. CONCLUSION: The multidimensional MRI time series is represented by the tensor tool and decomposed into low rank tensor terms and sparse tensor terms. The low rank spatial structure is captured by the adaptive ST-HOSVD for fast approximation and the sparse component is constrained efficiently with a sparsity transform and l1 norm. The optimization problem is solved by an iterative soft-thresholding algorithm. Through extensive 3D and 4D dMRI experiments, it is demonstrated that our method can achieve superior reconstruction performance and efficiency compared with the other three state-of-theart methods reported in the literature.

Improved robust tensor principal component analysis for accelerating dynamic MR imaging reconstruction.

Dynamic magnetic resonance imaging (dMRI) strikes a balance between reconstruction speed and image accuracy in medical imaging field. In this paper, an improved robust tensor principal component analysis (RTPCA) method is proposed to reconstruct the dynamic magnetic resonance imaging (MRI) from highly under-sampled K-space data. The MR reconstruction problem is formulated as a high-order low-rank tenor plus sparse tensor recovery problem, which is solved by robust tensor principal component analysis (RTPCA) with a new tensor nuclear norm (TNN). To further exploit the low-rank structures in multi-way data, the core matrix nuclear norm, extracted from the diagonal elements of the core tensor under tensor singular value decomposition (t-SVD) framework, is also integrated into TNN for enforcing the low-rank structure in MRI datasets. The experimental results show that the proposed method outperforms state-of-the-art methods in terms of both MR image reconstruction accuracy and computational efficiency on 3D and 4D experiment datasets, especially for 4D MR image reconstruction. Graphical abstract The flowchart of the proposed method to reconstruct the dynamic magnetic resonance imaging (MRI) from highly under-sampled K-space data in the kth iteration. To further exploit the low-rank structures in multi-way data, the core matrix nuclear norm, extracted from the diagonal elements of the core tensor under tensor singular value decomposition (t-SVD) framework, is also integrated into tensor nuclear norm (TNN) for enforcing the low-rank structure in MRI datasets. In each iteration, the first step is to get low-rank tensor ℓk - 1 by using soft thresholding on the singular values of ℓk - 1 = χk - 1 - ξk - 1, and an improved tensor nuclear norm method is proposed to process the low-rank tensor ℓk - 1 firstly. Then, the shrinkage operator is applied to ξk - 1 = χk - 1 - ℓk - 1 for sparse part ξk - 1. The final reconstructed d-MRI χk is obtained by enforcing data consistency that the residual in K-space is subtracted by the sum of the reconstructed low-rank tensor and sparse tensor.