Navigator-free EPI Ghost Correction with Structured Low-Rank Matrix Models: New Theory and Methods

Many EPI ghost correction methods are based on treating subsets of EPI data from different readout gradient polarities or different shots as if they were acquired from different "virtual coils" in a parallel imaging experiment. Structured low-rank matrix models have previously been introduced to enable calibrationless parallel imaging reconstruction, and such ideas have recently been extended to enable navigator-free EPI ghost correction. However, our theoretical analysis shows that, because of uniform subsampling, the corresponding optimization problems for EPI data will always have either undesirable or non-unique solutions in the absence of additional constraints. This theoretical analysis leads us to propose new problem formulations for navigator-free EPI that incorporate side information from either image-domain or k-space domain parallel imaging methods. The importance of using nonconvex low-rank matrix regularization is also identified. We demonstrate using phantom and in vivo data that the proposed methods are able to eliminate ghost artifacts for several navigator-free EPI acquisition schemes, obtaining better performance in comparison to state-of-the-art methods across a range of different scenarios, including both single-channel acquisition and highly accelerated multi-channel acquisition.