Further Development of Subspace Imaging to Magnetic Resonance Fingerprinting: A Low-rank Tensor Approach

Magnetic resonance fingerprinting is a recent quantitative MRI technique that simultaneously acquires multiple tissue parameter maps (e.g., T₁, T₂, and spin density) in a single imaging experiment. In our early work, we demonstrated that the low-rank/subspace reconstruction significantly improves the accuracy of tissue parameter maps over the conventional MR fingerprinting reconstruction that utilizes simple pattern matching. In this paper, we generalize the low-rank/subspace reconstruction by introducing a multilinear low-dimensional image model (i.e., a low-rank tensor model). With this model, we further estimate the subspace associated with magnetization evolutions to simplify the image reconstruction problem. The proposed formulation results in a nonconvex optimization problem which we solve by an alternating minimization algorithm. We evaluate the performance of the proposed method with numerical experiments, and demonstrate that the proposed method improves the conventional reconstruction method and the state-of-the-art low-rank reconstruction method.