# Two Datasets Are Better Than One: Method of Double Moments for 3-D Reconstruction in Cryo-EM

arXiv: https://arxiv.org/abs/2511.07438 · HTML: https://mlsanity.com/paper/2511.07438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 79 references that are in the map.
- First posted on arXiv 2 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Low-rank Solutions of Linear Matrix Equations via Procrustes Flow](https://mlsanity.com/paper/1507.03566/) (2015)
- [Estimation under group actions: recovering orbits from invariants](https://mlsanity.com/paper/1712.10163/) (2017)
- [Fast Steerable Principal Component Analysis](https://mlsanity.com/paper/1412.0781/) (2014)
- [Denoising and Covariance Estimation of Single Particle Cryo-EM Images](https://mlsanity.com/paper/1602.06632/) (2016)
- [Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles](https://mlsanity.com/paper/1907.05377/) (2019)
- [Centering noisy images with application to cryo-EM](https://mlsanity.com/paper/2009.04810/) (2020)
- [Maximum likelihood for high-noise group orbit estimation and single-particle cryo-EM](https://mlsanity.com/paper/2107.01305/) (2021)
- [3D ab initio modeling in cryo-EM by autocorrelation analysis](https://mlsanity.com/paper/1710.08076/) (2017)
- [Orthogonal Matrix Retrieval in Cryo-Electron Microscopy](https://mlsanity.com/paper/1412.0494/) (2014)
- [Anisotropic twicing for single particle reconstruction using autocorrelation analysis](https://mlsanity.com/paper/1704.07969/) (2017)
- [Ab-initio Contrast Estimation and Denoising of Cryo-EM Images](https://mlsanity.com/paper/2202.07737/) (2022)
- [Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography](https://mlsanity.com/paper/2207.02985/) (2022)
- [The sample complexity of sparse multi-reference alignment and single-particle cryo-electron microscopy](https://mlsanity.com/paper/2210.15727/) (2022)
- [Moment-based metrics for molecules computable from cryo-EM images](https://mlsanity.com/paper/2401.15183/) (2024)
- [Misspecified Maximum Likelihood Estimation for Non-Uniform Group Orbit Recovery](https://mlsanity.com/paper/2509.22945/) (2025)

## Abstract (arXiv)

Cryo-electron microscopy (cryo-EM) is a powerful imaging technique for reconstructing three-dimensional molecular structures from noisy tomographic projection images of randomly oriented particles. We introduce a new data fusion framework, termed the method of double moments (MoDM), which reconstructs molecular structures from two instances of the second-order moment of projection images obtained under distinct orientation distributions: one uniform, the other non-uniform and unknown. We prove that these moments generically uniquely determine the underlying structure, up to a global rotation and reflection, and we develop a convex-relaxation-based algorithm that achieves accurate recovery using only second-order statistics. Our results demonstrate the advantage of collecting and modeling multiple datasets under different experimental conditions, illustrating that leveraging dataset diversity can substantially enhance reconstruction quality in computational imaging tasks.