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Estimation in the Group Action Channel

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

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Abstract: We 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.
Publication Date: 2018
Citation: Abbe, E, Pereira, JM, Singer, A. (2018). Estimation in the Group Action Channel. 2018-June (561 - 565. doi:10.1109/ISIT.2018.8437646
DOI: doi:10.1109/ISIT.2018.8437646
Pages: 561 - 565
Type of Material: Conference Article
Journal/Proceeding Title: IEEE International Symposium on Information Theory - Proceedings
Version: Author's manuscript

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