ArticleProceedings of the National Academy of Sciences of the United States of America2023
Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Two datasets are better than one: method of double moments for 3D reconstruction in cryo-EM.Inverse problems · 2026Article
- Subspace Method of Moments forSIAM journal on imaging sciences · 2026Article
- Phase retrieval via gain-based photonic XY-Hamiltonian optimization.Communications physics · 2026Article
- FAST EXPANSION INTO HARMONICS ON THE BALL.SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics · 2025Article
- Structure determination using high-order spatial correlations in single-particle X-ray scattering.IUCrJ · 2024Article
- Moment-based metrics for molecules computable from cryogenic electron microscopy images.Biological imaging · 2024Article
- Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit.SIAM journal on imaging sciences · 2023Article
- Fast principal component analysis for cryo-electron microscopy images.Biological imaging · 2023Article
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5 authors.
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Abstract
The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we consider the effect of imposing sparsity priors on the molecule. We use techniques from signal processing, optimization, and applied algebraic geometry to obtain theoretical and computational contributions for this challenging nonlinear inverse problem with sparsity constraints. We prove that molecular structures modeled as sums of Gaussians are uniquely determined by the second-order autocorrelation of their projection images, implying that the sample complexity is proportional to the square of the variance of the noise. This theory improves upon the nonsparse case, where the third-order autocorrelation is required for uniformly oriented particle images and the sample complexity scales with the cube of the noise variance. Furthermore, we build a computational framework to reconstruct molecular structures which are sparse in the wavelet basis. This method combines the sparse representation for the molecule with projection-based techniques used for phase retrieval in X-ray crystallography.
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