Low tensor-train rank with total variation for magnetic resonance imaging reconstruction

The model by imposing the low-rank minimization has been proved to be effective for magnetic resonance imaging(MRI) completion. Recent studies have also shown that imposing tensor train(TT) and total variation(TV) constraint on tensor completion can produce impressive performance, and the lower TT-rank minimization constraint can be represented as the guarantee for global constraint, while the total variation as the guarantee for regional constraint. In our solution, a new approach is utilized to solve TT-TV model. In contrast with imposing the alternating linear scheme, nuclear norm regularization on TT-ranks is introduced in our method as it is an effective surrogate for rank optimization and our solution does not need to initialize and update tensor cores. By applying the alternating direction method of multipliers(ADMM), the optimization model is disassembled into some sub-problems, singular value thresholding can be used as the solution to the first sub-problem and soft thresholding can be used as the solution to the second sub-problem. The new optimization algorithm ensures the effectiveness of data recovery. In addition, a new method is introduced to reshape the MRI data to a higher-dimensional tensor, so as to enhance the performance of data completion. Furthermore, the method is compared with some other methods including tensor reconstruction methods and a matrix reconstruction method. It is concluded that the proposed method has a better recovery accuracy than others in MRI data according to the experiment results.