Feature detection and hypothesis testing for extremely noisy nanoparticle images using topological data analysis

TL;DR

This paper introduces a novel topological data analysis method using cubical persistent homology for detecting atomic features in extremely noisy nanoparticle images, enabling robust hypothesis testing and fluxional behavior analysis.

Contribution

It presents a flexible algorithm leveraging cubical persistent homology for feature detection and hypothesis testing in ultra low signal-to-noise ratio TEM images, with statistical guarantees.

Findings

Effective detection of atomic columns in noisy TEM images.

Monte Carlo goodness-of-fit testing validates feature significance.

Method provides univariate time series for fluxional behavior analysis.

Abstract

We propose a flexible algorithm for feature detection and hypothesis testing in images with ultra low signal-to-noise ratio using cubical persistent homology. Our main application is in the identification of atomic columns and other features in transmission electron microscopy (TEM). Cubical persistent homology is used to identify local minima and their size in subregions in the frames of nanoparticle videos, which are hypothesized to correspond to relevant atomic features. We compare the performance of our algorithm to other employed methods for the detection of columns and their intensity. Additionally, Monte Carlo goodness-of-fit testing using real valued summaries of persistence diagrams derived from smoothed images (generated from pixels residing in the vacuum region of an image) is developed and employed to identify whether or not the proposed atomic features generated by our algorithm are due to noise. Using these summaries derived from the generated persistence diagrams, one can produce univariate time series for the nanoparticle videos, thus providing a means for assessing fluxional behavior. A guarantee on the false discovery rate for multiple Monte Carlo testing of identical hypotheses is also established.