UNSUPERVISED PARTICLE SORTING FOR CRYO-EM USING PROBABILISTIC PCA Gili Weiss-DickerAmitay EldaryYoel ShkolinskyyTamir Bendory School of Electrical Engineering Tel Aviv University

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UNSUPERVISED PARTICLE SORTING FOR CRYO-EM USING PROBABILISTIC PCA

Gili Weiss-Dicker ?Amitay Eldar †Yoel Shkolinsky†Tamir Bendory?

?School of Electrical Engineering, Tel Aviv University

†Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University

ABSTRACT

Single-particle cryo-electron microscopy (cryo-EM) is a lead-

ing technology to resolve the structure of molecules. Early

in the process, the user detects potential particle images in

the raw data. Typically, there are many false detections as a

result of high levels of noise and contamination. Currently,

removing the false detections requires human intervention

to sort the hundred thousands of images. We propose a

statistically-established unsupervised algorithm to remove

non-particle images. We model the particle images as a union

of low-dimensional subspaces, assuming non-particle images

are arbitrarily scattered in the high-dimensional space. The

algorithm is based on an extension of the probabilistic PCA

framework to robustly learn a non-linear model of union of

subspaces. This provides a ﬂexible model for cryo-EM data,

and allows to automatically remove images that correspond

to pure noise and contamination. Numerical experiments

corroborate the effectiveness of the sorting algorithm.

Index Terms—Unsupervised learning, single-particle

cryo-EM, probabilistic PCA, expectation-maximization

1 INTRODUCTION

Single-particle cryo-electron microscopy (cryo-EM) is an

emerging technology to determine the structure of molecules.

In the cryo-EM process, the acquired “raw data” image, called

a micrograph, contains a few dozens of 2-D tomographic par-

ticle projection images with unknown random orientations

and locations. The micrograph suffers from low signal-to-

noise ratio (SNR), as low as 1

100 . Typically, it also contains

undesired contamination. For the purpose of this paper, the

pixels in a micrograph can be broadly divided into three cat-

egories: regions of particles with additive noise, regions of

contamination, and regions of noise only.

During the cryo-EM workﬂow, particle images are detected

and extracted from micrographs in a process called particle

picking [1, 2]. The extracted images are the individual parti-

cles within each micrograph. If only particles were picked,

the images chosen by the particle picker would have been

used to construct the 3-D molecular structure. Figure 1 illus-

trates a schematic sequence of computational steps typically

used to convert the raw data into 3-D molecular structures.

While many particle picking algorithms were developed, e.g.,

[3, 4, 5], due to very low SNR levels they result in contam-

ination and pure noise images picked along with the particle

images. Typical images chosen by a picking algorithm can be

seen in Figure 2.

A common approach to remove non-particle images, called

“2-D classiﬁcation,” is semi-automatic and involves an ex-

pert practitioner; it relies heavily on subjective criteria that

are neither consistent nor reproducible among different users.

We propose an automatic and statistically-established unsu-

pervised algorithm to remove non-particle images from the

data. Speciﬁcally, we assume that all particle images approx-

imately lie on a union of subspaces, whereas the non-particle

images are scattered in the high-dimensional space. Similar

parsimonious models are ubiquitous in many signal process-

ing tasks, and speciﬁcally in different stages of the cryo-EM

computational pipeline [7, 8]. The main computational tool

in this work is an extension of principal component analysis

(PCA). PCA has been applied to cryo-EM data for several

tasks [7, 9]. However, PCA is limited since it learns a single

subspace. We build on a maximum likelihood formulation,

called probabilistic PCA (PPCA) [10, 11, 12]. In particu-

lar, we iteratively estimate the union of subspaces using an

expectation-maximization (EM) algorithm, while sorting out

images that do not lie on the subspaces.

PPCA offers several attractive advantages over PCA. First,

PPCA can be readily extended to multiple subspaces, leading

to a nonlinear ﬂexible mixture model. Second, we work in the

dimension of the problem (i.e., the number of parameters that

deﬁne the sought subspaces) in contrast to standard PCA that

requires estimating the full covariance matrix.

Fig. 1: A typical data processing pipeline for single-particle cryo-EM. The main contribution of this work is the fully automated sorting block,

aiming to replace the need of an expert practitioner involved in the sorting step.

arXiv:2210.12811v2 [eess.IV] 7 Mar 2023

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UNSUPERVISEDPARTICLESORTINGFORCRYO-EMUSINGPROBABILISTICPCAGiliWeiss-Dicker?AmitayEldaryYoelShkolinskyyTamirBendory??SchoolofElectricalEngineering,TelAvivUniversityyDepartmentofAppliedMathematics,SchoolofMathematicalSciences,TelAvivUniversityABSTRACTSingle-particlecryo-electronmicroscopy(cryo-EM)isal...

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UNSUPERVISED PARTICLE SORTING FOR CRYO-EM USING PROBABILISTIC PCA Gili Weiss-DickerAmitay EldaryYoel ShkolinskyyTamir Bendory School of Electrical Engineering Tel Aviv University

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