论文标题
超分辨率多参考对齐
Super-resolution multi-reference alignment
论文作者
论文摘要
我们研究了超分辨率的多参考比对，这是估计许多循环，下采样和嘈杂观察的信号的问题。我们专注于低SNR制度，并表明当$ \ mathbb {r}^m $中的信号是唯一确定的，当每个观察值的数字$ l $是信号长度的平方根的顺序时，信号长度$（l = o（\ sqrt {m} {m}））$。更非正式地措辞可以使分辨率保持平衡。如果观测值与至少1/snr $^3 $成正比，则此结果将保持。相比之下，即使观察结果没有被下采样（$ l = m $），也不可能恢复观察结果。该分析结合了统计信号处理和不变理论的工具。我们设计了一种期望最大化算法，并证明它可以在具有挑战性的SNR制度中超级溶解信号。
We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled, and noisy observations. We focus on the low SNR regime, and show that a signal in $\mathbb{R}^M$ is uniquely determined when the number $L$ of samples per observation is of the order of the square root of the signal's length $(L=O(\sqrt{M}))$. Phrased more informally, one can square the resolution. This result holds if the number of observations is proportional to at least 1/SNR$^3$. In contrast, with fewer observations recovery is impossible even when the observations are not down-sampled ($L=M$). The analysis combines tools from statistical signal processing and invariant theory. We design an expectation-maximization algorithm and demonstrate that it can super-resolve the signal in challenging SNR regimes.
