TY - JOUR

T1 - Method of moments for 3D single particle ab initio modeling with non-uniform distribution of viewing angles

AU - Sharon, Nir

AU - Kileel, Joe

AU - Khoo, Yuehaw

AU - Landa, Boris

AU - Singer, Amit

N1 - Publisher Copyright:
© 2020 IOP Publishing Ltd.

PY - 2020

Y1 - 2020

N2 - Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3D structure of a molecule from several noisy 2D projections images taken at unknown viewing angles. Most reconstruction algorithms require a low-resolution initialization for the 3D structure, which is the goal of ab initio modeling. Suggested by Zvi Kam in 1980, the method of moments (MoM) offers one approach, wherein low-order statistics of the 2D images are computed and a 3D structure is estimated by solving a system of polynomial equations. Unfortunately, Kam's method suffers from restrictive assumptions, most notably that viewing angles should be distributed uniformly. Often unrealistic, uniformity entails the computation of higher-order correlations, as in this case first and second moments fail to determine the 3D structure. In the present paper, we remove this hypothesis, by permitting an unknown, non-uniform distribution of viewing angles in MoM. Perhaps surprisingly, we show that this case is statistically easier than the uniform case, as now first and second moments generically suffice to determine low-resolution expansions of the molecule. In the idealized setting of a known, non-uniform distribution, we find an efficient provable algorithm inverting first and second moments. For unknown, non-uniform distributions, we use non-convex optimization methods to solve for both the molecule and distribution.

AB - Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3D structure of a molecule from several noisy 2D projections images taken at unknown viewing angles. Most reconstruction algorithms require a low-resolution initialization for the 3D structure, which is the goal of ab initio modeling. Suggested by Zvi Kam in 1980, the method of moments (MoM) offers one approach, wherein low-order statistics of the 2D images are computed and a 3D structure is estimated by solving a system of polynomial equations. Unfortunately, Kam's method suffers from restrictive assumptions, most notably that viewing angles should be distributed uniformly. Often unrealistic, uniformity entails the computation of higher-order correlations, as in this case first and second moments fail to determine the 3D structure. In the present paper, we remove this hypothesis, by permitting an unknown, non-uniform distribution of viewing angles in MoM. Perhaps surprisingly, we show that this case is statistically easier than the uniform case, as now first and second moments generically suffice to determine low-resolution expansions of the molecule. In the idealized setting of a known, non-uniform distribution, we find an efficient provable algorithm inverting first and second moments. For unknown, non-uniform distributions, we use non-convex optimization methods to solve for both the molecule and distribution.

KW - Cryo-EM

KW - Wigner matrices

KW - ab initio modeling

KW - autocorrelation analysis

KW - method of moments

KW - non-convex optimization

KW - spherical harmonics

UR - http://www.scopus.com/inward/record.url?scp=85080946281&partnerID=8YFLogxK

U2 - 10.1088/1361-6420/ab6139

DO - 10.1088/1361-6420/ab6139

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AN - SCOPUS:85080946281

SN - 0266-5611

VL - 36

JO - Inverse Problems

JF - Inverse Problems

IS - 4

M1 - 044003

ER -