Multitaper estimation on arbitrary domains
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Multitaper estimators have enjoyed significant success in providing spectral density estimates from finite samples. Unfortunately, highly accurate methods exist only for certain symmetric acquisition domains, such as rectangles or disks. Methods proposed for arbitrary domains suffer from the instability inherent in calculating the necessary Slepian tapers to high precision. Finally, no performance bounds are currently available to measure the mean squared error of the estimate. This is inadequate for applications such as cryo-electron microscopy, where accurate noise models must be estimated from irregular domains with small sample sizes. To remedy this, we prove a set of performance bounds for the multitaper estimator on arbitrary domains. We also introduce randomized tapers, a proxy for the Slepian tapers yielding the same spectral estimate but which can be calculated to arbitrary precision. The method is demonstrated on synthetic and experimental datasets from cryo-electron microscopy, where it reduces mean squared error by a factor of two or more compared to traditional methods.
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