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

Abstract 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.