Simultaneous Non-Convex Low Rank Regularization for Fast Magnetic Resonance Spectroscopy Reconstruction

2D magnetic resonance spectroscopy (MRS) is extensively used to analyze the components, structures, and interactions of substances in chemistry and bioengineering. To reduce data acquisition time, the spatiotemporally encoded ultrafast (STEU) MRS employs a fast means to acquire data in the hybrid time and frequency (HTF) plane, but relies on non-uniform sampling (NUS) technique. After that, a proper reconstruction method is essential to recover a high quality 2D MRS from undersampled HTF data. In this work, each column and row of 2D MRS are converted into Hankel matrices, by which a simultaneous low rank regularization model is proposed to exploit the bivariate exponential structure of 2D MRS signal. Additionally, a non-convex surrogate function for rank is integrated in the proposed model to more precisely enforce the low rank property of Hankel matrices. To ensure computational accuracy and convergence, an efficient numerical algorithm is further deduced based on alternating direction method of multipliers (ADMM) iteration. The experimental results have shown that the proposed method significantly outperforms existing 2D MRS reconstruction methods, and presents a strong robustness to low sampling rates, various sampling patterns, and measurement noise with a favorable complexity