A caveat in using trajectories with long readout durations are artefacts due to B0 inhomogeneity. Correcting these based on B0-maps or reverse-phase-encoded EPI requires additional scan time and is unattractive for some applications. In this work, the capability of coil-arrays to extrapolate information in k-space is shown to also allow the extraction of temporal information such as the time-varying phase introduced by B0-offsets. An optimization problem is formulated to retrieve an estimate of B0 from measured data without making assumptions on the employed trajectory. B0 estimation and self-correction of single-shot spiral and EPI in-vivo data (up to R=4) is demonstrated.