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This article aims at developing a model based optimization for reduction oftemporal unwrapping and field estimation errors in multi-echo acquisition ofGradient Echo sequence. Using the assumption that the phase is linear along thetemporal dimension, the field estimation is performed by application of unityrank approximation to the Hankel matrix formed using the complex exponential ofthe channel combined phase at each echo time. For the purpose of maintainingconsistency with the observed complex data, the linear phase evolution model isformulated as an optimization problem with a cost function that involves afidelity term and a unity rank prior, implemented using alternatingminimization. Itoh s algorithm applied to the multi-echo phase estimated fromthis linear phase evolution model is able to reduce the unwrapping errors ascompared to the unwrapping when directly applied to the measured phase.Secondly, the improved accuracy of the frequency fit in comparison toestimation using weighted least-square regression and penalized maximumlikelihood is demonstrated using numerical simulation of field perturbation dueto magnetic susceptibility effect. It is shown that the field can be estimatedwith 80 percent reduction in mean absolute error in comparison to wLSR and 66percent reduction with respect to penalized maximum likelihood. The improvementin performance becomes more pronounced with increasing strengths of fieldgradient magnitudes and echo spacing.

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