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.