Model‐informed unsupervised deep learning approaches to frequency and phase correction of MRS signals

PURPOSE: A supervised deep learning (DL) approach for frequency and phase correction (FPC) of MRS data recently showed encouraging results, but obtaining transients with labels for supervised learning is challenging. This work investigates the feasibility and efficiency of unsupervised deep learning–based FPC. METHODS: Two novel deep learning–based FPC methods (deep learning–based Cr referencing and deep learning–based spectral registration), which use a priori physics domain knowledge, are presented. The proposed networks were trained, validated, and evaluated using simulated, phantom, and publicly accessible in vivo MEGA‐edited MRS data. The performance of our proposed FPC methods was compared with other generally used FPC methods, in terms of precision and time efficiency. A new measure was proposed in this study to evaluate the FPC method performance. The ability of each of our methods to carry out FPC at varying SNR levels was evaluated. A Monte Carlo study was carried out to investigate the performance of our proposed methods. RESULTS: The validation using low‐SNR manipulated simulated data demonstrated that the proposed methods could perform FPC comparably with other methods. The evaluation showed that the deep learning–based spectral registration over a limited frequency range method achieved the highest performance in phantom data. The applicability of the proposed method for FPC of GABA‐edited in vivo MRS data was demonstrated. Our proposed networks have the potential to reduce computation time significantly. CONCLUSIONS: The proposed physics‐informed deep neural networks trained in an unsupervised manner with complex data can offer efficient FPC of large MRS data in a shorter time.