TY - GEN

T1 - Estimation in the Group Action Channel

AU - Abbe, Emmanuel

AU - Pereira, Joao M.

AU - Singer, Amit

N1 - Funding Information:
ACKNOWLEDGMENTS EA was partly supported by the NSF CAREER Award CCF–1552131, ARO grant W911NF–16–1–0051 and NSF Center for the Science of Information CCF–0939370. JP and AS were partially supported by Award Number R01GM090200 from the NIGMS, the Simons Foundation Investigator Award and Simons Collaborations on Algorithms and Geometry, the Moore Foundation Data-Driven Discovery Investigator Award, and AFOSR FA9550-17-1-0291.

PY - 2018/8/15

Y1 - 2018/8/15

N2 - 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.

AB - 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.

KW - Chapman-Robbins bound

KW - Cryo-EM

KW - Multi-reference alignment

UR - http://www.scopus.com/inward/record.url?scp=85052430431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052430431&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2018.8437646

DO - 10.1109/ISIT.2018.8437646

M3 - Conference contribution

AN - SCOPUS:85052430431

SN - 9781538647806

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 561

EP - 565

BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018

Y2 - 17 June 2018 through 22 June 2018

ER -