SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1565-1594, January 2020.
Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian tapers is only tractable for certain symmetric domains, such as rectangles or disks. In addition, no performance bounds are currently available for the mean squared error of the spectral density estimate. This situation is inadequate for applications such as cryo-electron microscopy, where noise models must be estimated from irregular domains with small sample sizes. We show that the multitaper estimator only depends on the linear space spanned by the tapers. As a result, Slepian tapers may be replaced by proxy tapers spanning the same subspace (validating the common practice of using partially converged solutions to the Slepian eigenproblem as tapers). These proxies may consequently be calculated using standard numerical algorithms for block diagonalization. We also prove a set of performance bounds for multitaper estimators on arbitrary domains. The method is demonstrated on synthetic and experimental datasets from cryo-electron microscopy, where it reduces the mean squared error by a factor of two or more compared to traditional methods.

中文翻译：

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任意域上的多锥估计

SIAM影像科学杂志，第13卷，第3期，第1565-1594页，2020年1月。
多锥估计器在使用在采集域上定义的Slepian函数作为锥度从有限样本估计光谱密度方面取得了巨大的成功。不幸的是，这些Slepian锥度的数值计算仅适用于某些对称域，例如矩形或磁盘。另外，当前没有性能界限可用于频谱密度估计的均方误差。对于诸如冷冻电子显微镜之类的应用来说，这种情况是不适当的，在这些应用中，必须从不规则域中以小样本量估算噪声模型。我们表明，多锥度估计量仅取决于锥度所跨越的线性空间。结果是，Slepian锥度可以用跨越相同子空间的代理锥度来代替（验证使用Slepian本征问题的部分收敛解作为锥度的通用做法）。因此，可以使用用于块对角化的标准数值算法来计算这些代理。我们还证明了任意域上多锥估计的一组性能边界。该方法在低温电子显微镜的合成和实验数据集上得到了证明，与传统方法相比，该方法将均方误差降低了两倍或更多。