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Lederman, Roy R; Singer, Amit
Continuously heterogeneous hyper-objects in cryo-EM and 3-Đ movies of many temporal dimensions Technical Report
no. arXiv:1704.02899 [cs], 2017, (arXiv: 1704.02899).
Abstract | Links | BibTeX | Tags: Computer Science - Computer Vision and Pattern Recognition, cryo-EM, heterogeneity, HyperMolecules
@techreport{lederman_continuously_2017,
title = {Continuously heterogeneous hyper-objects in cryo-EM and 3-Đ movies of many temporal dimensions},
author = {Roy R Lederman and Amit Singer},
url = {http://arxiv.org/abs/1704.02899},
year = {2017},
date = {2017-04-01},
urldate = {2020-08-13},
number = {arXiv:1704.02899 [cs]},
abstract = {Single particle cryo-electron microscopy (EM) is an increasingly popular method for determining the 3-D structure of macromolecules from noisy 2-D images of single macromolecules whose orientations and positions are random and unknown. One of the great opportunities in cryo-EM is to recover the structure of macromolecules in heterogeneous samples, where multiple types or multiple conformations are mixed together. Indeed, in recent years, many tools have been introduced for the analysis of multiple discrete classes of molecules mixed together in a cryo-EM experiment. However, many interesting structures have a continuum of conformations which do not fit discrete models nicely; the analysis of such continuously heterogeneous models has remained a more elusive goal. In this manuscript, we propose to represent heterogeneous molecules and similar structures as higher dimensional objects. We generalize the basic operations used in many existing reconstruction algorithms, making our approach generic in the sense that, in principle, existing algorithms can be adapted to reconstruct those higher dimensional objects. As proof of concept, we present a prototype of a new algorithm which we use to solve simulated reconstruction problems.},
note = {arXiv: 1704.02899},
keywords = {Computer Science - Computer Vision and Pattern Recognition, cryo-EM, heterogeneity, HyperMolecules},
pubstate = {published},
tppubtype = {techreport}
}
Lederman, Roy R; Singer, Amit
A Representation Theory Perspective on Simultaneous Alignment and Classification Technical Report
no. arXiv:1607.03464 [cs, math], 2016, (arXiv: 1607.03464).
Abstract | Links | BibTeX | Tags: Algorithms, Computer Science - Computer Vision and Pattern Recognition, cryo-EM, Mathematics - Optimization and Control, Representation Theory
@techreport{lederman_representation_2016,
title = {A Representation Theory Perspective on Simultaneous Alignment and Classification},
author = {Roy R Lederman and Amit Singer},
url = {http://arxiv.org/abs/1607.03464},
year = {2016},
date = {2016-07-01},
urldate = {2021-01-22},
number = {arXiv:1607.03464 [cs, math]},
abstract = {One of the difficulties in 3D reconstruction of molecules from images in single particle Cryo-Electron Microscopy (Cryo-EM), in addition to high levels of noise and unknown image orientations, is heterogeneity in samples: in many cases, the samples contain a mixture of molecules, or multiple conformations of one molecule. Many algorithms for the reconstruction of molecules from images in heterogeneous Cryo-EM experiments are based on iterative approximations of the molecules in a non-convex optimization that is prone to reaching suboptimal local minima. Other algorithms require an alignment in order to perform classification, or vice versa. The recently introduced Non-Unique Games framework provides a representation theoretic approach to studying problems of alignment over compact groups, and offers convex relaxations for alignment problems which are formulated as semidefinite programs (SDPs) with certificates of global optimality under certain circumstances. In this manuscript, we propose to extend Non-Unique Games to the problem of simultaneous alignment and classification with the goal of simultaneously classifying Cryo-EM images and aligning them within their respective classes. Our proposed approach can also be extended to the case of continuous heterogeneity.},
note = {arXiv: 1607.03464},
keywords = {Algorithms, Computer Science - Computer Vision and Pattern Recognition, cryo-EM, Mathematics - Optimization and Control, Representation Theory},
pubstate = {published},
tppubtype = {techreport}
}