Estimation in the Group Action Channel

Emmanuel Abbe, Joao M. Pereira, Amit Singer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

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.

Original languageEnglish (US)
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages561-565
Number of pages5
ISBN (Print)9781538647806
DOIs
StatePublished - Aug 15 2018
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: Jun 17 2018Jun 22 2018

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2018-June
ISSN (Print)2157-8095

Other

Other2018 IEEE International Symposium on Information Theory, ISIT 2018
CountryUnited States
CityVail
Period6/17/186/22/18

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Chapman-Robbins bound
  • Cryo-EM
  • Multi-reference alignment

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  • Cite this

    Abbe, E., Pereira, J. M., & Singer, A. (2018). Estimation in the Group Action Channel. In 2018 IEEE International Symposium on Information Theory, ISIT 2018 (pp. 561-565). [8437646] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2018.8437646