https://3demmethods.i2pc.es/index.php?action=history&feed=atom&title=2018Boumal_SinglePass 2026-06-13T12:13:45Z Revision history for this page on the wiki MediaWiki 1.44.2 https://3demmethods.i2pc.es/index.php?title=2018Boumal_SinglePass&diff=3476&oldid=prev 2019-04-16T05:49:04Z

<p>Created page with &quot;== Citation == Boumal, N.; Bendory, T.; Lederman, R. R. &amp; Singer, A. Heterogeneous multireference alignment: A single pass approach. Proc. 52nd Annual Conf. Information Scien...&quot;</p> <p><b>New page</b></p><div>== Citation ==<br /> <br /> Boumal, N.; Bendory, T.; Lederman, R. R. &amp; Singer, A. Heterogeneous multireference alignment: A single pass approach. Proc. 52nd Annual Conf. Information Sciences and Systems (CISS), 2018, 1-6<br /> <br /> == Abstract ==<br /> <br /> 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.<br /> <br /> == Keywords ==<br /> <br /> == Links ==<br /> <br /> https://ieeexplore.ieee.org/abstract/document/8362313<br /> <br /> == Related software ==<br /> <br /> == Related methods ==<br /> <br /> == Comments ==</div>

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