Multi-target Detection with an Arbitrary Spacing Distribution
arXiv:1905.03176 · doi:10.1109/TSP.2020.2975943
Abstract
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.
arXiv comment13 pages, 8 figures
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Cited by in corpus (6)
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- Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms
- Two-dimensional multi-target detection: an autocorrelation analysis approach
- An approximate expectation-maximization for two-dimensional multi-target detection
- Image recovery from rotational and translational invariants
- Generalized autocorrelation analysis for multi-target detection