Echo planar imaging (EPI) is an ultrafast magnetic resonance imaging (MRI) technique that allows one to acquire a 2D image in about 100 ms. Unfortunately, the standard EPI images suffer from substantial geometric distortions, mainly originating from susceptibility differences in adjacent tissues. To reduce EPI distortions, correction methods based on a field map, which is a map of the off-resonance frequencies, have been developed. In this work, a nonlinear least squares estimator is used to optimize the estimation of the field map of the B(0) field. The model of the EPI and reference data includes parameters for the phase evolution, the complex magnitude, the relaxation of the MRI signal and the EPI-specific phase difference between odd and even echoes, and from these parameters, additional corrections might be computed. The reference data required to estimate the field map can be acquired with a modified EPI-sequence. The proposed method is tested on simulated as well as experimental data and proves to be significantly more robust against noise, compared to the previously suggested method.
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