TY - JOUR

T1 - Autocorrelation analysis for cryo-EM with sparsity constraints

T2 - Improved sample complexity and projection-based algorithms

AU - Bendory, Tamir

AU - Khoo, Yuehaw

AU - Kileel, Joe

AU - Mickelin, Oscar

AU - Singer, Amit

N1 - Funding Information:
ACKNOWLEDGMENTS. TB is supported in part by the ISF grant no. 1924/21, the BSF grant no. 2020159, and the NSF-BSF grant no. 2019752. JK is supported in part by start-up grants from the College of Natural Sciences and Oden Institute for Computational Engineering and Sciences at UT Austin. AS is supported in part by AFOSR FA9550-20-1-0266, the Simons Foundation Math+X Investigator Award, NSF BIGDATA IIS-1837992, NSF DMS-2009753, and NIH/NIGMS 1R01GM136780-01. JK thanks João M. Pereira for useful conversations. We would like to thank the editor and two anonymous reviewers whose suggestions improved the paper.
Publisher Copyright:
Copyright © 2023 the Author(s).

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - crystallographic phase retrieval

KW - method of moments

KW - projection-based algorithm

KW - single-particle cryoelectron microscopy

KW - sparsity

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U2 - 10.1073/pnas.2216507120

DO - 10.1073/pnas.2216507120

M3 - Article

C2 - 37094135

AN - SCOPUS:85153687691

SN - 0027-8424

VL - 120

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 118

M1 - e2216507120

ER -