A linear phase evolution model for reduction of temporal unwrapping and field estimation errors in multi-echo GRE

This article aims at developing a model based optimization for reduction of temporal unwrapping and field estimation errors in multi-echo acquisition of Gradient Echo (GRE) sequence. Using the assumption that the phase is linear along the temporal dimension, the field estimation is performed by application of unity rank approximation (URA) to the Hankel matrix formed using the complex exponential of the channel-combined phase at each echo time. For the purpose of maintaining consistency with the observed complex data, the linear phase evolution (LPE) model is formulated as an optimization problem with a cost function that involves a fidelity term and a unity rank prior, implemented using alternating minimization. Itoh’s algorithm applied to the multi-echo phase estimated from this LPE model is able to reduce the unwrapping errors as compared to the unwrapping when directly applied to the measured phase. Secondly, the improved accuracy of the frequency fit in comparison to estimation using weighted least-square regression (wLSR) and penalized maximum likelihood (pML) is demonstrated using numerical simulation of field perturbation due to magnetic susceptibility effect. It is shown that the field can be estimated with 80% reduction in mean absolute error (MAE) in comparison to wLSR and 66% reduction with respect to pML. The improvement in performance becomes more pronounced with increasing strengths of field gradient magnitudes and echo spacing.

💡 Research Summary

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The paper presents a novel model‑based optimization framework aimed at reducing temporal phase‑unwrapping errors and improving field‑map estimation in multi‑echo gradient‑echo (GRE) MRI. The authors start from the physical observation that, for a given voxel, the complex GRE signal can be written as
 s(TE) = ρ·exp