Optimal rates of estimation for multi-reference alignment
Statistics Theory
2018-05-22 v2 Statistics Theory
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.
Cite
@article{arxiv.1702.08546,
title = {Optimal rates of estimation for multi-reference alignment},
author = {Afonso S. Bandeira and Philippe Rigollet and Jonathan Weed},
journal= {arXiv preprint arXiv:1702.08546},
year = {2018}
}