# Bias and variance reduction and denoising for CTF Estimation

## TL;DR

This paper introduces a novel CTF estimation method for electron microscopy images that reduces bias and variance using multi-taper spectral estimation and leverages known properties of the CTF to improve accuracy.

## Contribution

The proposed method combines multi-taper spectral estimation with known CTF properties to enhance the accuracy of CTF estimation in electron microscopy images.

## Key findings

- Captures zero-crossings of the CTF in low-mid frequencies
- Reduces bias and variance in spectral estimates
- Improves CTF estimation accuracy

## Abstract

When using an electron microscope for imaging of particles embedded in vitreous ice, the objective lens will inevitably corrupt the projection images. This corruption manifests as a band-pass filter on the micrograph. In addition, it causes the phase of several frequency bands to be flipped and distorts frequency bands. As a precursor to compensating for this distortion, the corrupting point spread function, which is termed the contrast transfer function (CTF) in reciprocal space, must be estimated. In this paper, we will present a novel method for CTF estimation. Our method is based on the multi-taper method for power spectral density estimation, which aims to reduce the bias and variance of the estimator. Furthermore, we use known properties of the CTF and of the background of the power spectrum to increase the accuracy of our estimation. We will show that the resulting estimates capture the zero-crossings of the CTF in the low-mid frequency range.