  Robustness against data inconsistencies, imaging artifacts and acquisition
speed are crucial factors limiting the possible range of applications for
magnetic resonance imaging (MRI). Therefore, we report a novel calibrationless
parallel imaging technique which simultaneously estimates coil profiles and
image content in a relaxed forward model. Our method is robust against a wide
class of data inconsistencies, minimizes imaging artifacts and is comparably
fast combining important advantages of many conceptually different
state-of-the-art parallel imaging approaches. Depending on the experimental
setting, data can be undersampled well below the Nyquist limit. Here, even high
acceleration factors yield excellent imaging results while being robust to
noise and the occurrence of phase singularities in the image domain, as we show
on different data. Moreover, our method successfully reconstructs acquisitions
with insufficient field-of-view. We further compare our approach to ESPIRiT and
SAKE using spin-echo and gradient echo MRI data from the human head and knee.
In addition, we show its applicability to non-Cartesian imaging on radial FLASH
cardiac MRI data. Using theoretical considerations, we show that ENLIVE can be
related to a low-rank formulation of blind multi-channel deconvolution,
explaining why it inherently promotes low-rank solutions.
