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arXiv 1801.04366cs.ITmath.IT
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群作用信道中的估计

Estimation in the group action channel

Emmanuel Abbe, João M. Pereira, Amit Singer

摘要:

我们分析的问题,估计信号从多个测量上的$\mbox{group action channel}$,线性变换信号由一个随机组的行动,然后由一个固定的投影和加性高斯噪声。该通道的动机是多参考对准和低温电子显微镜等应用。我们专注于这些应用中普遍存在的大噪声制度。我们给出了信号轨道的任何渐近无偏估计的均方误差(MSE)的下界,这意味着当$N/σ^{2d}$从上面有界时,MSE从0有界,其中$N$是观测值的数量,$σ$是噪声标准差,$d$是所谓的$\mbox{moment order cutoff}$。相反,最大似然估计是一致的,如果$N /σ^{2d}$发散。

英文摘要:

We analyze the problem of estimating a signal from multiple measurements on a $\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryo-electron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the signal's orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away from 0 when $N/σ^{2d}$ is bounded from above, where $N$ is the number of observations, $σ$ is the noise standard deviation, and $d$ is the so-called $\mbox{moment order cutoff}$. In contrast, the maximum likelihood estimator is shown to be consistent if $N /σ^{2d}$ diverges.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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