On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Near-optimal algorithms for unique games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Unique games on expanding constraint graphs are easy: extended abstract
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
Spectral Algorithms for Unique Games
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Probabilistic analysis of the semidefinite relaxation detector in digital communications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Design of Approximation Algorithms
The Design of Approximation Algorithms
Using multilayer perceptrons to align high range resolution radar signals
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
IEEE Transactions on Information Theory
Extension of phase correlation to subpixel registration
IEEE Transactions on Image Processing
Exact recovery of sparsely-used dictionaries
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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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.