Accelerated dynamic MR imaging with joint balanced low-rank tensor and sparsity constraints

Dynamic magnetic resonance imaging (DMRI) is an essential medical imaging technique, but the slow data acquisition process limits its further development.

By exploiting the inherent spatio-temporal correlation of MR images, low-rank tensor based methods have been developed to accelerate imaging. However, the tensor rank used by these methods is defined by an unbalanced matricization scheme, which cannot capture the global correlation of DMR data efficiently during the reconstruction process.

In this paper, an effective reconstruction model is proposed to achieve accurate reconstruction by using the tensor train (TT) rank defined by a well-balanced matricization scheme to exploit the hidden correlation of DMR data and combining sparsity. Meanwhile, the ket augmentation (KA) technology is introduced to preprocess the DMR data into a higher-order tensor through block structure addressing, which further improves the ability of TT rank to explore the local information of the image. In order to solve the proposed model, the alternating direction method of multipliers (ADMM) is used to decompose the optimization problem into several unconstrained subproblems.

The performance of the proposed method was validated on the 3D DMR image dataset by using different sampling trajectories and sampling rates. Extensive numerical experiments demonstrate that the reconstruction quality of the proposed method is superior to several state-of-the-art reconstruction methods.

The proposed method successfully utilizes the TT rank to explore the global correlation of DMR images, enabling more detailed information of the image to be captured. Besides, with the sparse priors, the proposed method can further improve the overall reconstruction quality for highly undersampled MR images.