School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou, 310018, People's Republic of China.
Department of Clinical Engineering, the Second Affiliated Hospital, School of Medicine, Zhejiang University, Hangzhou, 310019, People's Republic of China.
Med Biol Eng Comput. 2020 Jul;58(7):1483-1498. doi: 10.1007/s11517-020-02161-5. Epub 2020 May 5.
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 ℓ by using soft thresholding on the singular values of ℓ = χ - ξ, and an improved tensor nuclear norm method is proposed to process the low-rank tensor ℓ firstly. Then, the shrinkage operator is applied to ξ = χ - ℓ for sparse part ξ. The final reconstructed d-MRI χ 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.
动态磁共振成像（dMRI）在医学成像领域在重建速度和图像准确性之间取得了平衡。在本文中，提出了一种改进的鲁棒张量主成分分析（RTPCA）方法，用于从高度欠采样的 K 空间数据中重建动态磁共振成像（MRI）。MR 重建问题被表述为一个高阶低秩张量加稀疏张量恢复问题，该问题通过具有新张量核范数（TNN）的鲁棒张量主成分分析（RTPCA）来解决。为了进一步利用多向数据中的低秩结构，从张量奇异值分解（t-SVD）框架下的核张量对角元素中提取的核心矩阵核范数也被集成到 TNN 中，以在 MRI 数据集中强制实施低秩结构。实验结果表明，该方法在 3D 和 4D 实验数据集上的磁共振图像重建准确性和计算效率方面均优于最先进的方法，特别是在 4D MR 图像重建方面。
