Multi-dimensional low rank plus sparse decomposition for reconstruction of under-sampled dynamic MRI

In this paper, we introduce a multi-dimensional approach to the problem of reconstruction of MR image sequences that are highly undersampled in k-space. By formulating the reconstruction as a high-order low rank tensor plus sparse tensor decomposition problem, we propose an efficient numerical algorithm based on the alternating direction method of multipliers (ADMM) to solve the optimization. Using Tucker representation, the sparse component is learnt efficiently with different sparsifying matrices along the modes of dynamic MR data. To estimate the low rank tensor, a convex cost function is defined to be the weighted sum of nuclear norms of its 3 unfolding matrices. Through extensive experimental results we show that our proposed method achieves superior reconstruction quality, compared to the state-of-the-art reconstruction methods.