The acquisition of dynamic magnetic resonance imaging often requires a long time. For acceleration, how to improve the quality of reconstruction from a limited set of under-samples is a crucial problem. The low-rank plus sparse decomposition model, which is also called robust principal component analysis (RPCA), is widely used for reconstruction of dynamic magnetic resonance imag- ing (MRI) data in an unsupervised way. In this paper, considering that dynamic MRI data is naturally in tensor form with block-wise smoothness, we propose a smooth robust tensor principal component analysis (SRTPCA) method for the dynamic magnetic resonance image reconstruction. Compared with classical RPCA ways, the low rank and sparsity terms are extended to tensor space to fully exploit the spatial and temporal data structures. Moreover, a tensor total variation regularization term is used to encourage the multi-dimensional block- wise smoothness for the reconstructed dynamic MRI data. The relaxed convex optimization model can be divided into several sub-problems by the alternating direction method of multipliers algorithm. Numerical experiments on cardiac perfusion and cine datasets demonstrate that the proposed SRTPCA method outperforms the state-of-the-art ones in terms of recovery accuracy.

The datasets used in this paper are all online available, you can obtain it through the link described as follows:

• the cardiac perfusion dataset with the size 128×128×40 (https://www.cai2r.net/resources/software/ls-reconstruction-matlab-code), rename the dataset as pref_128_40 and put it to directory “Dataset”
• the cardiac cine dataset with the size 256×256×30 (http://www.doc.ic.ac.uk/~jc1006/software.html), rename the dataset as cine_256_30 and put it to directory “Dataset”.

Yipeng Liu, Tengteng Liu, Jiani Liu, Ce Zhu, "Smooth Robust Tensor Principal Component Analysis for Compressed Sensing of Dynamic MRI ," Pattern Recognition, vol. 102, no. 107252, 2020. DOI: 10.1016/j.patcog.2020.107252