TY - JOUR
T1 - Heterogeneous multireference alignment for images with application to 2D classification in single particle reconstruction
AU - Ma, Chao
AU - Bendory, Tamir
AU - Boumal, Nicolas
AU - Sigworth, Fred
AU - Singer, Amit
N1 - Funding Information:
Manuscript received October 12, 2018; revised July 12, 2019 and September 23, 2019; accepted September 25, 2019. Date of publication October 10, 2019; date of current version November 27, 2019. This work was supported in part by the National Institute of General Medical Sciences (NIGMS) under Grant R01GM090200, in part by the Air Force Office of Scientific Research (AFOSR) under Grant FA9550-17-1-0291, in part by the Simons Foundation Math + X Investigator Award, and in part by the Moore Foundation Data-Driven Discovery Investigator Award. The work of N. Boumal was supported in part by the NSF Award under Grant DMS-1719558. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Dong Xu. (Corresponding author: Chao Ma.) C. Ma and T. Bendory are with the Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544 USA (e-mail: chaom@princeton.edu).
Publisher Copyright:
© 1992-2012 IEEE.
PY - 2020
Y1 - 2020
N2 - Motivated by the task of 2D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating individual rotations is challenging. We propose a framework to estimate the target images directly from the observations, completely bypassing the need to cluster or register the images. The framework consists of two steps. First, we estimate rotation-invariant features of the images, such as the bispectrum. These features can be estimated to any desired accuracy, at any noise level, provided sufficiently many observations are collected. Then, we estimate the images from the invariant features. Numerical experiments on synthetic cryo-EM datasets demonstrate the effectiveness of the method. Ultimately, we outline future developments required to apply this method to experimental data.
AB - Motivated by the task of 2D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating individual rotations is challenging. We propose a framework to estimate the target images directly from the observations, completely bypassing the need to cluster or register the images. The framework consists of two steps. First, we estimate rotation-invariant features of the images, such as the bispectrum. These features can be estimated to any desired accuracy, at any noise level, provided sufficiently many observations are collected. Then, we estimate the images from the invariant features. Numerical experiments on synthetic cryo-EM datasets demonstrate the effectiveness of the method. Ultimately, we outline future developments required to apply this method to experimental data.
KW - Multireference alignment
KW - bispectrum
KW - cryo-EM
KW - single particle reconstruction
KW - steerable PCA
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U2 - 10.1109/TIP.2019.2945686
DO - 10.1109/TIP.2019.2945686
M3 - Article
C2 - 31613760
AN - SCOPUS:85077493343
SN - 1057-7149
VL - 29
SP - 1699
EP - 1710
JO - IEEE Transactions on Image Processing
JF - IEEE Transactions on Image Processing
M1 - 8864095
ER -