PURPOSE: Combining MR phase images from multiple receive coils is a challenging problem, complicated by ambiguities introduced by phase wrapping, noise, and the unknown phase-offset between the coils. Various techniques have been proposed to mitigate the effect of these ambiguities but most of the existing methods require additional reference scans and/or use ad hoc post-processing techniques that do not guarantee any optimality. THEORY AND METHODS: Here, the phase estimation problem is formulated rigorously using a maximum-likelihood (ML) approach. The proposed framework jointly designs the acquisition-processing chain: the optimized pulse sequence is a single multiecho gradient echo scan and the corresponding postprocessing algorithm is a voxel-per-voxel ML estimator of the underlying tissue phase. RESULTS: Our proposed framework (Maximum AmbiGuity distance for Phase Imaging, MAGPI) achieves substantial improvements in the phase estimate, resulting in phase signal-to-noise ratio (SNR) gains by up to an order of magnitude compared to existing methods. CONCLUSION: The advantages of MAGPI are: (1) ML-optimal combination of phase data from multiple receive coils, without a reference scan; (2) voxel-per-voxel ML-optimal estimation of the underlying tissue phase, without the need for phase unwrapping or image smoothing; and (3) robust dynamic estimation of channel-dependent phase-offsets.

We have previously proposed a novel magnetic resonance (MR) phase imaging framework (MAGPI) based on a three-echo sequence that demonstrated substantial gains in phase signal-to-noise ratio (SNR). We improve upon the performance of MAGPI by extending the formulation to handle (i) an alternating gradient polarity (bipolar) readout scheme and (ii) an arbitrary number of echoes. We formulate the phase-imaging problem using maximum-likelihood (ML) estimation. The acquisition uses an optimized multi-echo gradient echo (MEGE) sequence. The tissue-phase estimation algorithm is a voxel-per-voxel approach, which requires no reference scans, no phase unwrapping and no spatial denoising. Unlike other methods, our bipolar readout model is general and does not make simplifying assumptions about the even-odd echo phase errors. The results show that (a) our proposed bipolar MAGPI approach improves on the phase SNR gains achieved with monopolar MAGPI and (b) the phase SNR converges with the number of echoes more rapidly with bipolar MAGPI. Importantly, bipolar MAGPI enables phase imaging in severely SNR-constrained scenarios, where monopolar MAGPI is unable to find solutions. The substantial phase SNR gains achieved with our framework are used here to (a) accelerate acquisitions (full brain 0.89 mm in-plane resolution in 2 min 30 sec) and (b) enable high-contrast high-resolution phase imaging (310 µm in-plane resolution) at clinical field strengths. Copyright © 2016 John Wiley & Sons, Ltd.