Wavelet invariants for statistically robust multireference alignment
Abstract
We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multireference alignment problem and generalizations thereof, we analyze the statistical properties of this representation given a large number of independent corruptions of a target signal. We prove the nonlinear wavelet based representation uniquely defines the power spectrum but allows for an unbiasing procedure that cannot be directly applied to the power spectrum. After unbiasing the representation to remove the effects of the additive noise and random dilations, we recover an approximation of the power spectrum by solving a convex optimization problem, and thus obtain the target signal up to an unknown phase. Extensive numerical experiments demonstrate the statistical robustness of this approximation procedure.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.11062
 Bibcode:
 2019arXiv190911062H
 Keywords:

 Electrical Engineering and Systems Science  Signal Processing;
 Mathematics  Statistics Theory;
 62
 EPrint:
 53 pages, 8 figures