Unsupervised deep learning model for correcting Nyquist ghosts of single-shot spatiotemporal encoding

Purpose: To design an unsupervised deep learning (DL) model for correcting Nyquist ghosts of single-shot spatiotemporal encoding (SPEN) and evaluate the model for real MRI applications. Methods: The proposed method consists of three main components: (1) an unsupervised network that combines Residual Encoder and Restricted Subspace Mapping (RERSM-net) and is trained to generate a phase-difference map based on the even and odd SPEN images; (2) a spin physical forward model to obtain the corrected image with the learned phase difference map; and (3) cycle-consistency loss that is explored for training the RERSM-net. Results: The proposed RERSM-net could effectively generate smooth phase difference maps and correct Nyquist ghosts of single-shot SPEN. Both simulation and real in vivo MRI experiments demonstrated that our method outperforms the state-of-the-art SPEN Nyquist ghost correction method. Furthermore, the ablation experiments of generating phase-difference maps show the advantages of the proposed unsupervised model. Conclusion: The proposed method can effectively correct Nyquist ghosts for the single-shot SPEN sequence.