Andén Joakim, Singer Amit
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544.
Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544.
Int Conf Sampl Theory Appl SampTA. 2017 Jul;2017:169-173. doi: 10.1109/SAMPTA.2017.8024447. Epub 2017 Sep 4.
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy.
功率谱估计是许多应用中的重要工具，例如噪声白化。流行的多窗方法取得了显著成功，但对于样本较少的短信号却失效。我们提出一种统计模型，其中信号由固定但未知的随机源的随机线性组合给出。给定多个这样的信号，我们估计由这些固定源的功率谱所张成的子空间。将各个功率谱估计投影到该子空间上可提高估计精度。我们为该方法提供了精度保证，并在低温电子显微镜的模拟数据和实验数据上进行了验证。
