We propose an extension to Regularized Non-Linear Inversion (NLINV), which simultaneously reconstructs multiple images and sets of coil sensitivity profiles. This method, termed ENLIVE (Extended Non-Linear InVersion inspired by ESPIRiT), can be related to a convex relaxation of the NLINV problem subject to a low-rank constraint. From NLINV, it inherits its suitability for calibrationless and non-Cartesian imaging; from ESPIRiT it inherits robustness to data inconsistencies.
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