Smooth robust tensor principal component analysis for compressed sensing of dynamic MRI

Dynamic magnetic resonance imaging (DMRI) often requires a long time for measurement acquisition, and it is a crucial problem about the enhancement of reconstruction quality from a limited set of under-samples. The low-rank plus sparse decomposition model, which is also called robust principal component analysis (RPCA), is widely used for reconstruction of DMRI data in the model-based way. In this paper, considering that DMRI data are naturally in tensor form with block-wise smoothness, we propose a smooth robust tensor principal component analysis (SRTPCA) method for DMRI reconstruction. Compared with classical RPCA approaches, the low rank and sparsity terms are extended to tensor versions 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 DMRI data. The relaxed convex optimization model can be divided into several sub-problems by the alternating direction method of multipliers. 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.