TY - JOUR
T1 - The Generalized Method of Moments for Multi-Reference Alignment
AU - Abas, Asaf
AU - Bendory, Tamir
AU - Sharon, Nir
N1 - Publisher Copyright:
© 1991-2012 IEEE.
PY - 2022
Y1 - 2022
N2 - This paper studies the application of the generalized method of moments (GMM) to multi-reference alignment (MRA): the problem of estimating a signal from its circularly-translated and noisy copies. We begin by proving that the GMM estimator maintains its asymptotic optimality for statistical models with group symmetry, including MRA. Then, we conduct a comprehensive numerical study and show that the GMM substantially outperforms the classical method of moments, whose application to MRA has been studied thoroughly in the literature. We also formulate the GMM to estimate a three-dimensional molecular structure using cryo-electron microscopy and present numerical results on simulated data.
AB - This paper studies the application of the generalized method of moments (GMM) to multi-reference alignment (MRA): the problem of estimating a signal from its circularly-translated and noisy copies. We begin by proving that the GMM estimator maintains its asymptotic optimality for statistical models with group symmetry, including MRA. Then, we conduct a comprehensive numerical study and show that the GMM substantially outperforms the classical method of moments, whose application to MRA has been studied thoroughly in the literature. We also formulate the GMM to estimate a three-dimensional molecular structure using cryo-electron microscopy and present numerical results on simulated data.
KW - Generalized method of moments
KW - multi-reference alignment
KW - orbit recovery problem
KW - single-particle cryo-electron microscopy
UR - http://www.scopus.com/inward/record.url?scp=85126332497&partnerID=8YFLogxK
U2 - 10.1109/TSP.2022.3157483
DO - 10.1109/TSP.2022.3157483
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AN - SCOPUS:85126332497
SN - 1053-587X
VL - 70
SP - 1377
EP - 1388
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
ER -