The Generalized Method of Moments for Multi-Reference Alignment

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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.

Original languageEnglish
Pages (from-to)1377-1388
Number of pages12
JournalIEEE Transactions on Signal Processing
StatePublished - 2022


  • Generalized method of moments
  • multi-reference alignment
  • orbit recovery problem
  • single-particle cryo-electron microscopy

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


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