https://3demmethods.i2pc.es/index.php?action=history&feed=atom&title=2020Lederman_representation 2026-05-24T20:15:41Z Revision history for this page on the wiki MediaWiki 1.44.2 https://3demmethods.i2pc.es/index.php?title=2020Lederman_representation&diff=3808&oldid=prev 2020-08-19T09:11:31Z

<p>Created page with &quot;== Citation == Lederman, R. R.; Singer, A. A representation theory perspective on simultaneous alignment and classification. Applied and Computational Harmonic Analysis, 2020...&quot;</p> <p><b>New page</b></p><div>== Citation ==<br /> <br /> Lederman, R. R.; Singer, A. A representation theory perspective on simultaneous alignment and classification. Applied and Computational Harmonic Analysis, 2020, 49, 1001-1024 <br /> <br /> == Abstract ==<br /> <br /> Single particle cryo-electron microscopy (EM) is a method for determining the 3-D structure of macromolecules from many noisy 2-D projection images of individual macromolecules whose orientations and positions are random and unknown. The problem of orientation assignment for the images motivated work on multireference alignment. The recent non-unique games framework provides a representation theoretic approach to alignment over compact groups, and offers a convex relaxation with certificates of global optimality in some cases. One of the great opportunities in cryo-EM is studying heterogeneous samples, containing two or more distinct conformations of molecules. Taking advantage of this opportunity presents an algorithmic challenge: determining both the class and orientation of each particle. We generalize multireference alignment to a problem of alignment and classification, and 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 classes. <br /> <br /> == Keywords ==<br /> <br /> == Links ==<br /> <br /> https://www.sciencedirect.com/science/article/pii/S1063520319301034<br /> <br /> == Related software ==<br /> <br /> == Related methods ==<br /> <br /> == Comments ==</div>

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