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

TL;DR

This paper introduces a new theoretical framework for navigator-free EPI ghost correction using structured low-rank matrix models, highlighting the need for additional constraints and side information to ensure unique solutions, and demonstrates improved artifact removal in practical MRI data.

Contribution

The paper provides a novel theoretical analysis of structured low-rank models for EPI ghost correction, emphasizing the importance of constraints and side information, and proposes improved methods with demonstrated benefits.

Findings

Proposed methods effectively eliminate ghost artifacts in EPI imaging.

Incorporating side information improves solution uniqueness and reconstruction quality.

Nonconvex low-rank regularization enhances ghost correction performance.

Abstract

Structured low-rank matrix models have previously been introduced to enable calibrationless MR image reconstruction from sub-Nyquist data, and such ideas have recently been extended to enable navigator-free echo-planar imaging (EPI) ghost correction. This paper presents novel theoretical analysis which shows that, because of uniform subsampling, the structured low-rank matrix optimization problems for EPI data will always have either undesirable or non-unique solutions in the absence of additional constraints. This theory leads us to recommend and investigate 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 \emph{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. Results are shown for both single-channel acquisition and highly accelerated multi-channel acquisition.