Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f:\mathbb{R}\to\mathbb{R}$ from many observations that have been randomly translated and corrupted by additive noise. We consider a generalization of classic MRA where signals are also corrupted by a random scale change, i.e. dilation. We propose a novel data-driven unbiasing procedure which can recover an unbiased estimator of the bispectrum of the unknown signal, given knowledge of the dilation distribution. Lastly, we invert the recovered bispectrum to achieve full signal recovery, and validate our methodology on a set of synthetic signals.

中文翻译：

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用于膨胀不变多参考对齐的双谱无偏


受冷冻电子显微镜等现代数据应用的推动，经典多参考对准 (MRA) 的目标是恢复未知信号$f:\mathbb{R}\到\mathbb{R}$来自许多被随机转换并被附加噪声破坏的观察结果。我们考虑经典 MRA 的推广，其中信号也会因随机尺度变化（即膨胀）而损坏。我们提出了一种新颖的数据驱动的无偏过程，它可以在已知膨胀分布的情况下恢复未知信号双谱的无偏估计量。最后，我们反转恢复的双谱以实现完全信号恢复，并在一组合成信号上验证我们的方法。