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 SNR${}^{-3}$ in the low SNR regime.

中文翻译：

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任意间距分布的多目标检测

受单粒子低温电子显微镜中的结构重建问题的启发，我们考虑了多目标检测模型，其中目标信号的多个副本在长时间测量中出现在未知位置，并被加性高斯噪声进一步破坏。在低噪声水平下，人们可以很容易地检测到信号的出现并通过平均来估计信号。然而，在存在高噪声的情况下，这是本文的重点，检测是不可能的。在这里，我们提出了两种方法——自相关分析和近似期望最大化算法——来重建信号，而无需检测测量中的信号出现。特别是，我们的方法适用于信号出现的任意间隔分布。