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Multi-electrode arrays such as "Neuropixels" probes enable the study of neuronal voltage signals at high temporal and single-cell spatial resolution. However, in vivo recordings from these devices often experience some shifting of the probe (due e.g. to animal movement), resulting in poorly localized voltage readings that in turn can corrupt estimates of neural activity. We introduce a new registration method to partially correct for this motion. In contrast to previous template-based registration methods, the proposed approach is decentralized, estimating shifts of the data recorded in multiple timebins with respect to one another, and then extracting a global registration estimate from the resulting estimated shift matrix. We find that the resulting decentralized registration is more robust and accurate than previous template-based approaches applied to both simulated and real data, but nonetheless some significant non-stationarity in the recovered neural activity remains that should be accounted for by downstream processing pipelines. Open source code is available at https://github.com/evarol/NeuropixelsRegistration.