# Multi-target Detection with an Arbitrary Spacing Distribution

arXiv: https://arxiv.org/abs/1905.03176 · HTML: https://mlsanity.com/paper/1905.03176/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2019.

## Built on by (most cited first, 2 of 2)

- [Multi-target detection with rotations](https://mlsanity.com/paper/2101.07709/) (2021)
- [Score-based diffusion priors for multi-target detection](https://mlsanity.com/paper/2312.08500/) (2023)

## Abstract (arXiv)

Motivated by the structure reconstruction problem in single-particle cryo-electron microscopy, we consider the multi-target detection model, where multiple copies of a target signal occur at unknown locations in a long measurement, further corrupted by additive Gaussian noise. At low noise levels, one can easily detect the signal occurrences and estimate the signal by averaging. However, in the presence of high noise, which is the focus of this paper, detection is impossible. Here, we propose two approaches---autocorrelation analysis and an approximate expectation maximization algorithm---to reconstruct the signal without the need to detect signal occurrences in the measurement. In particular, our methods apply to an arbitrary spacing distribution of signal occurrences. We demonstrate reconstructions with synthetic data and empirically show that the sample complexity of both methods scales as 1/SNR^3 in the low SNR regime.