Non-local tensor sparse representation and tensor low rank regularization for dynamic MRI reconstruction

Dynamic Magnetic Resonance Imaging (DMRI) reconstruction is a challenging theme in image processing. A variety of dimensionality reduction methods using vectorization have been proposed. However, most of them gave rise to a loss of spatial and temporal information. To deal with this problem, this article develops a DMRI reconstruction method in a nonlocal framework by integrating the nonlocal sparse tensor with low-rank tensor regularization. The sparsity constraint employs the Tucker decomposition tensor sparse representation, and the t-product-based tensor nuclear norm is used to set the low-rank constraint. Both constraints are handled in a nonlocal framework, which can take advantage of data redundancy in DMRI. Furthermore, the nonlocal sparse tensor representation we proposed constructs a tensor dictionary in the spatio-temporal dimension, making sparsity more efficient. Consequently, our method can better exploit the multi-dimensional coherence of DMRI data due to its sparsity and lowrankness and the fact that it uses a different tensor decomposition-based method. The Alternating Direction Method of Multipliers (ADMM) has been used for optimization. Experimental results show that the performance of the proposed method is superior to several conventional methods.