While the formation of ghost-free images from EPI data can be a difficult problem, recent low-rank matrix modeling methods have demonstrated promising results. In this abstract, we provide new theoretical insight into these approaches, and show that the low-rank ghost correction optimization problem has infinitely many solutions without using additional constraints. However, we also show that SENSE-like or GRAPPA-like constraints can be successfully used to make the problem well-posed, even for single-channel data. Additionally, we show that substantial performance gains can be achieved over previous low-rank ghost correction implementations by using nonconvex low-rank regularization instead of previous convex approaches.
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