Abstract
In this paper, we establish optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal processing, image processing, and computer vision, among others. We describe how this model can be viewed as a multivariate Gaussian mixture model under the constraint that the centers belong to the orbit of a group. This enables us to derive matching upper and lower bounds that feature an interesting dependence on the signal-to-noise ratio of the model. Both upper and lower bounds are articulated around a tight local control of Kullback–Leibler divergences that showcases the central role of moment tensors in this problem.
Original language | English (US) |
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Pages (from-to) | 25-75 |
Number of pages | 51 |
Journal | Mathematical Statistics and Learning |
Volume | 2 |
Issue number | 1 |
DOIs | |
State | Published - 2019 |
Keywords
- mixtures of Gaussians
- Multi-reference alignment
- orbit retrieval
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Signal Processing
- Statistics and Probability
- Theoretical Computer Science