# Rates of estimation for high-dimensional multi-reference alignment

@inproceedings{Dou2022RatesOE, title={Rates of estimation for high-dimensional multi-reference alignment}, author={Zehao Dou and Zhou Fan and Harrison H. Zhou}, year={2022} }

We study the continuous multi-reference alignment model of estimating a periodic function on the circle from noisy and circularly-rotated observations. Motivated by analogous high-dimensional problems that arise in cryo-electron microscopy, we establish minimax rates for estimating generic signals that are explicit in the dimension K . In a high-noise regime with noise variance σ 2 & K , the rate scales as σ 6 and has no further dependence on the dimension. This rate is achieved by a bispectrum…

## 2 Citations

### The sample complexity of sparse multi-reference alignment and single-particle cryo-electron microscopy

- Computer Science
- 2022

The second moment of the MRA and cryo-EM models is analyzed, showing that in both models the second moment determines the signal up to a set of unitary matrices, whose dimension is governed by the decomposition of the space of signals into irreducible representations of the group.

### Multi-target detection with rotations

- Computer ScienceInverse Problems and Imaging
- 2022

This work considers the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image and uses autocorrelation analysis to estimate rotationally and translationally invariant features of thetarget image.

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