RFuGE –an accelerated imaging method combining Parallel Transmit RF encoding plus Gradient Encoding with compressed sensing reconstruction

Introduction: In compressed sensing, a problem with random phase encoding patterns is that the eddy current performance is much worse and can lead to significant artefacts because the resulting k-space distortions may be very different on adjacent k-space samples. This undermines performance in random sampling strategies. We have explored combining regular gradient sampling with randomly selected radio-frequency encoding achieved using a parallel transmit approach. This work has been stimulated by two developments: 1) constrained random sampling patterns consisting of a regular base sample distribution with a +/-1 Δk jitter has been demonstrated to perform as well as a more fully random sets of phase encodes for moderate to high sampling factors (up to 5-fold undersampling)[1][2], and 2) parallel transmit technology can provide effective spatial encoding by generating distinct RF field (B1) patterns that impose appropriate spatial phase variations [3]. Method: Parallel transmission allows spatial control of B1 a degree of freedom which in the past has not been available. These RF fields can be varied to effect the phase across the object FOV. This approach could be used to achieve the performance of the jittered undersample patterns without any eddy current effects. However, the linear phase variation that corresponds to a pure shift in k-space is hard to achieve in combination with uniform flip angle and can result in greatly elevated RF drive levels, which limits the applicability of this simple extension to gradient encoding. We therefore consider a more general approach, in which a set of K distinct RF field patterns are produced that have spatially varying phase structure, uniform flip angle and low SAR. To ensure that a basis set of patterns are distinct from one another we design each around a narrow strip phase ramp with a unique direction, but allow the rest of the field of view to vary freely consistent with a uniform excitation. We then adopt a regular subsampled gradient pattern and for each gradient step apply a randomly selected choice from these RF basis functions. We call this type of encoding RF plus Gradient Encoding, (RFuGE) and employ a Compressed Sensing style reconstruction [4] designed to exploit the random element in the data structure. Provided the signal remains sparse in itself or in transform domain an exact reconstruction may be achieved. To proceed we construct an exact forward model of RFuGE that predicts the data given an object and knowledge of the RF basis set: