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.

中文翻译：

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改进的鲁棒张量主成分分析，用于加速动态MR成像重建。

动态磁共振成像（dMRI）在医学成像领域实现了重建速度和图像准确性之间的平衡。本文提出了一种改进的鲁棒张量主成分分析（RTPCA）方法，以从高度欠采样的K空间数据中重建动态磁共振成像（MRI）。MR重建问题被公式化为高阶低阶次幂加稀疏张量恢复问题，通过具有新张量核规范（TNN）的鲁棒张量主成分分析（RTPCA）解决了该问题。为了进一步利用多路数据中的低秩结构，在张量奇异值分解（t-SVD）框架下从核心张量的对角元素提取的核心矩阵核范数也被集成到TNN中以强制执行MRI数据集中的排名结构。实验结果表明，在3D和4D实验数据集上，特别是4D MR图像重建方面，该方法在MR图像重建精度和计算效率方面均优于最新方法。图形摘要在第k次迭代中，从高度欠采样的K空间数据重建动态磁共振成像（MRI）的方法流程图。为了进一步利用多路数据中的低秩结构，在张量奇异值分解（t-SVD）框架下从核心张量的对角元素提取的核心矩阵核规范也被整合到张量核规范（TNN）中）来增强MRI数据集中的低级结构。在每次迭代中 第一步是通过对softk-1 =χk-1-ξk-1的奇异值进行软阈值获得低秩张量ork-1，并提出了一种改进的张量核范数方法来处理低秩张量ℓk-1首先。然后，将收缩算子应用于稀疏部分ξk-1的ξk-1 =χk-1-ℓk-1。通过加强数据一致性（通过用K减去K空间中的残差）来获得最终重建的d-MRIχk。重构的低秩张量和稀疏张量之和。