### 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 language | English (US) |
---|---|

Title of host publication | 2018 IEEE International Symposium on Information Theory, ISIT 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 561-565 |

Number of pages | 5 |

ISBN (Print) | 9781538647806 |

DOIs | |

State | Published - Aug 15 2018 |

Event | 2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States Duration: Jun 17 2018 → Jun 22 2018 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
---|---|

Volume | 2018-June |

ISSN (Print) | 2157-8095 |

### Other

Other | 2018 IEEE International Symposium on Information Theory, ISIT 2018 |
---|---|

Country | United States |

City | Vail |

Period | 6/17/18 → 6/22/18 |

### 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

## Fingerprint Dive into the research topics of 'Estimation in the Group Action Channel'. Together they form a unique fingerprint.

## Cite this

*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