Provable Method of Moments for Cryo-EM
Abstract
We study the recovery of a three-dimensional volume in single-particle cryo-electron microscopy (cryo-EM) from noisy tomographic projections acquired at unknown viewing rotations, drawn independently and uniformly from SO(3). We show that, in a spherical-shell representation satisfying an explicit shell-separation condition, the first three moments generically determine the underlying real volume up to its intrinsic global O(3) ambiguity. The proof is constructive and yields a frequency-marching procedure that successively recovers the volume. Consequently, consistent recovery in the high-noise regime has sample complexity n=ω(σ6), where n is the number of observations and σ2 is the noise variance. Numerical experiments validate the constructive recovery scheme under finite sampling and additive noise, and indicate that direct third-moment optimization can succeed beyond the structural assumptions required by the constructive proof.
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BibTeX
@misc{balanov2026provable,
title = {{Provable Method of Moments for Cryo-EM}},
author = {Amnon Balanov and Tamir Bendory and Dan Edidin and Josh Katz and Shay Kreymer and Nir Sharon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17892},
eprint = {2610.17892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17892},
}
RIS
TY - UNPB
TI - Provable Method of Moments for Cryo-EM
AU - Amnon Balanov
AU - Tamir Bendory
AU - Dan Edidin
AU - Josh Katz
AU - Shay Kreymer
AU - Nir Sharon
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17892
UR - https://arxiv.org/abs/2610.17892
AB - We study the recovery of a three-dimensional volume in single-particle cryo-electron microscopy (cryo-EM) from noisy tomographic projections acquired at unknown viewing rotations, drawn independently and uniformly from SO(3). We show that, in a spherical-shell representation satisfying an explicit shell-separation condition, the first three moments generically determine the underlying real volume up to its intrinsic global O(3) ambiguity. The proof is constructive and yields a frequency-marching procedure that successively recovers the volume. Consequently, consistent recovery in the high-noise regime has sample complexity n=ω(σ^6), where n is the number of observations and σ^2 is the noise variance. Numerical experiments validate the constructive recovery scheme under finite sampling and additive noise, and indicate that direct third-moment optimization can succeed beyond the structural assumptions required by the constructive proof.
ER -