Noise Estimation on Arbitrary Domains

Estimating the power spectra of a stochastic process is important for several data processing tasks, such image denoising/whitening. We consider the case where data is only observed on a limited spatial domain, which is seen in practice in cryo-EM and the geosciences. In this seminar we will first explain why a naive estimator of the noise power spectral density on this domain (i.e. taking a discrete Fourier transform and squaring) is biased. We will then introduce some alternative methods that give better noise estimates. This talk will not assume any prior background in signal processing or applications.