Undistorted MRI B0 fieldmap estimation using an augmented space

In MRI, multiple applications require knowledge of the inhomogeneity field map, such as off-resonance correction, susceptibility mapping, water-fat separation, and spectroscopy imaging. Standard fieldmap estimation methods produce results that are themselves distorted by the fieldmap. This is because it is assumed that the signal is instantaneously acquired at the echo time, which is only valid for short readouts. In this paper, we describe a general method to estimate an undistorted fieldmap using two or more echoes of the imaging sequence without the need of additional scanning. The proposed method is based on solving the inverse problem from the signal equation using the signal and - in contrast to standard methods - the timemap information. A discretization of the inverse problem using an augmented space is proposed and the discretized problem is solved using ℓ¹ optimization. The method was tested both in silico and in real data for EPI and Spiral imaging. The results show that the estimated fieldmap is accurate and has a better performance than the Phase Subtraction method when the off-resonance effects are large. Indeed, for simulations in single shot EPI acquisitions the normalized root mean square error (NRMSE) is 30% smaller than Phase Subtraction and in 5-interleaf Spiral the NRMSE is 20% smaller.