NDLI: Multireference alignment using semidefinite programming

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Multireference alignment using semidefinite programming

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Multireference alignment using semidefinite programming

Content Provider	ACM Digital Library
Author	Bandeira, Afonso S. Singer, Amit Zhu, Andy Charikar, Moses
Abstract	The multireference alignment problem consists of estimating a signal from multiple noisy shifted observations. Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which approximates the maximum likelihood estimator (MLE) for the multireference alignment problem. Although we show this MLE problem is Unique-Games hard to approximate within any constant, we observe that our poly-time approximation algorithm for this problem appears to perform quite well in typical instances, outperforming existing methods. In an attempt to explain this behavior we provide stability guarantees for our SDP under a random noise model on the observations. This case is more challenging to analyze than traditional semi-random instances of Unique-Games: the noise model is on vertices of a graph and translates into dependent noise on the edges. Interestingly, we show that if certain positivity constraints in the relaxation are dropped, its solution becomes equivalent to performing phase correlation, a popular method used for pairwise alignment in imaging applications. Finally, we describe how symmetry reduction techniques from matrix representation theory can greatly decrease the computational cost of the SDP considered.
Starting Page	459
Ending Page	470
Page Count	12
File Format	PDF
ISBN	9781450326988
DOI	10.1145/2554797.2554839
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-01-12
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Multireference alignment Unique-games Semidefinite relaxation Phase correlation
Content Type	Text
Resource Type	Article

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