# Robust and Efficient Parametric Spectral Estimation in Atomic Force Microscopy

## TL;DR

This paper introduces a robust two-stage spectral estimation method for atomic force microscopy data, significantly improving accuracy and noise robustness while reducing computational costs.

## Contribution

It presents a novel two-stage estimator combining variance stabilization and periodicity testing to enhance spectral parameter estimation in AFM data.

## Key findings

- Two- to ten-fold reduction in mean squared error
- Robustness against electronic noise
- Efficient parameter estimation with reduced computational cost

## Abstract

An atomic force microscope (AFM) is capable of producing ultra-high resolution measurements of nanoscopic objects and forces. It is an indispensable tool for various scientific disciplines such as molecular engineering, solid-state physics, and cell biology. Prior to a given experiment, the AFM must be calibrated by fitting a spectral density model to baseline recordings. However, since AFM experiments typically collect large amounts of data, parameter estimation by maximum likelihood can be prohibitively expensive. Thus, practitioners routinely employ a much faster least-squares estimation method, at the cost of substantially reduced statistical efficiency. Additionally, AFM data is often contaminated by periodic electronic noise, to which parameter estimates are highly sensitive. This article proposes a two-stage estimator to address these issues. Preliminary parameter estimates are first obtained by a variance-stabilizing procedure, by which the simplicity of least-squares combines with the efficiency of maximum likelihood. A test for spectral periodicities then eliminates high-impact outliers, considerably and robustly protecting the second-stage estimator from the effects of electronic noise. Simulation and experimental results indicate that a two- to ten-fold reduction in mean squared error can be expected by applying our methodology.