# Factor Analysis for Spectral Estimation

## TL;DR

This paper introduces a subspace projection method for spectral estimation that improves accuracy for short signals by leveraging a statistical model of fixed sources, with demonstrated success in cryo-electron microscopy data.

## Contribution

It proposes a novel subspace-based spectral estimation technique with theoretical guarantees, addressing limitations of existing methods for short signals.

## Key findings

- Enhanced spectral estimation accuracy for short signals.
- Theoretical guarantees for the proposed method.
- Successful application to cryo-electron microscopy data.

## Abstract

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.