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Boumal, N; Bendory, T; Lederman, Roy R; Singer, A

Heterogeneous multireference alignment: A single pass approach Inproceedings

In: 2018 52nd Annual Conference on Information Sciences and Systems (CISS), pp. 1–6, 2018.

Abstract | Links | BibTeX | Tags: bispectrum, concave programming, cryo-EM, cyclic shifts, Discrete Fourier transforms, estimation theory, expectation-maximization, Gaussian mixture models, heterogeneity, heterogeneous MRA, Heterogeneous multireference alignment, Multireference alignment, Noise measurement, non-convex optimization, nonconvex optimization problem, Optimization, Reliability, signal estimation, signal processing, Signal resolution, Signal to noise ratio, single pass approach, Standards

@inproceedings{boumal_heterogeneous_2018,

title = {Heterogeneous multireference alignment: A single pass approach},

author = {N Boumal and T Bendory and Roy R Lederman and A Singer},

doi = {10.1109/CISS.2018.8362313},

year = {2018},

date = {2018-01-01},

booktitle = {2018 52nd Annual Conference on Information Sciences and Systems (CISS)},

pages = {1--6},

abstract = {Multireference alignment (MRA) is the problem of estimating a signal from many noisy and cyclically shifted copies of itself. In this paper, we consider an extension called heterogeneous MRA, where K signals must be estimated, and each observation comes from one of those signals, unknown to us. This is a simplified model for the heterogeneity problem notably arising in cryo-electron microscopy. We propose an algorithm which estimates the K signals without estimating either the shifts or the classes of the observations. It requires only one pass over the data and is based on low-order moments that are invariant under cyclic shifts. Given sufficiently many measurements, one can estimate these invariant features averaged over the K signals. We then design a smooth, non-convex optimization problem to compute a set of signals which are consistent with the estimated averaged features. We find that, in many cases, the proposed approach estimates the set of signals accurately despite non-convexity, and conjecture the number of signals K that can be resolved as a function of the signal length L is on the order of √L.},

keywords = {bispectrum, concave programming, cryo-EM, cyclic shifts, Discrete Fourier transforms, estimation theory, expectation-maximization, Gaussian mixture models, heterogeneity, heterogeneous MRA, Heterogeneous multireference alignment, Multireference alignment, Noise measurement, non-convex optimization, nonconvex optimization problem, Optimization, Reliability, signal estimation, signal processing, Signal resolution, Signal to noise ratio, single pass approach, Standards},

pubstate = {published},

tppubtype = {inproceedings}

}