Multiple Low-Ranks plus Sparsity based Tensor Reconstruction for Dynamic MRI

Dynamic magnetic resonance imaging (DMRI) sequence can be represented as the sum of a low-rank component and a sparse tensor component. To exploit the low rank structure in multi-way data, the current works use either the Tucker rank or the CANDECOMP/PARAFAC (CP) rank for the low rank tensor component. In fact, these two kinds of tensor ranks represent different structures in high-dimensional data. In this paper, We propose a multiple low ranks plus sparsity based tensor reconstruction method for DMRI. The simultaneous minimization of both CP and Tucker ranks can better exploit multi-dimensional coherence in the low rank component of DMRI data, and the sparse component is regularized by the tensor total variation minimization. The reconstruction optimization model can be divided into two sub-problems to iteratively calculate the low rank and sparse components. For the sub-problem about low rank tensor component, the rank-one tensor updating and sum of nuclear norm minimization methods are used to solve it. To obtain the sparse tensor component, the primal dual method is used. We compare the proposed method with four state-of-the-art ones, and experimental results show that the proposed method can achieve better reconstruction quality than state-of-the-art ones.