# Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes

arXiv: https://arxiv.org/abs/1907.01898 · HTML: https://mlsanity.com/paper/1907.01898/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 5 of 5)

- [CryoBench: Diverse and challenging datasets for the heterogeneity problem in cryo-EM](https://mlsanity.com/paper/2408.05526/) (2024)
- [Ab-initio Contrast Estimation and Denoising of Cryo-EM Images](https://mlsanity.com/paper/2202.07737/) (2022)
- [Mixture of neural fields for heterogeneous reconstruction in cryo-EM](https://mlsanity.com/paper/2412.09420/) (2024)
- [Cryo-EM as a Stochastic Inverse Problem](https://mlsanity.com/paper/2509.05541/) (2025)
- [SOLVAR: Fast covariance-based heterogeneity analysis with pose refinement for cryo-EM](https://mlsanity.com/paper/2602.17603/) (2026)

## Abstract (arXiv)

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.