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 - 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
UR - http://www.scopus.com/inward/record.url?scp=85153687691&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85153687691&partnerID=8YFLogxK
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 -