Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms

Tamir Bendory, Yuehaw Khoo, Joe Kileel, Oscar Mickelin, Amit Singer

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Article numbere2216507120
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number118
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General


  • crystallographic phase retrieval
  • method of moments
  • projection-based algorithm
  • single-particle cryoelectron microscopy
  • sparsity


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