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Estimation in the Group Action Channel

Author(s): Abbe, Emmanuel; Pereira, JM; Singer, Amit

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dc.contributor.authorAbbe, Emmanuel-
dc.contributor.authorPereira, JM-
dc.contributor.authorSinger, Amit-
dc.date.accessioned2021-10-08T20:16:12Z-
dc.date.available2021-10-08T20:16:12Z-
dc.date.issued2018en_US
dc.identifier.citationAbbe, E, Pereira, JM, Singer, A. (2018). Estimation in the Group Action Channel. 2018-June (561 - 565. doi:10.1109/ISIT.2018.8437646en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1s561-
dc.description.abstractWe analyze the problem of estimating a signal from multiple measurements on a group action channel that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryo-electron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away from 0 when N/\sigma-{2d} is bounded from above, where N is the number of observations, \sigma is the noise standard deviation, and d is the so-called moment order cutoff. In contrast, the maximum likelihood estimator is shown to be consistent if N/\sigma-{2d} diverges.en_US
dc.format.extent561 - 565en_US
dc.language.isoen_USen_US
dc.relation.ispartofIEEE International Symposium on Information Theory - Proceedingsen_US
dc.rightsAuthor's manuscripten_US
dc.titleEstimation in the Group Action Channelen_US
dc.typeConference Articleen_US
dc.identifier.doidoi:10.1109/ISIT.2018.8437646-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/conference-proceedingen_US

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