# Periodic Artifact Reduction in Fourier transforms of Full Field Atomic Resolution Images

arXiv: https://arxiv.org/abs/2210.09024 · HTML: https://mlsanity.com/paper/2210.09024/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 22 references that are in the map.
- First posted on arXiv 14 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [Beware of Aliases -- Signal Preservation is Crucial for Robust Image Restoration](https://mlsanity.com/paper/2406.07435/) (2024)

## Abstract (arXiv)

The discrete Fourier transform is among the most routine tools used in high-resolution scanning / transmission electron microscopy (S/TEM). However, when calculating a Fourier transform, periodic boundary conditions are imposed and sharp discontinuities between the edges of an image cause a cross patterned artifact along the reciprocal space axes. This artifact can interfere with the analysis of reciprocal lattice peaks of an atomic resolution image. Here we demonstrate that the recently developed Periodic Plus Smooth Decomposition technique provides a simple, efficient method for reliable removal of artifacts caused by edge discontinuities. In this method, edge artifacts are reduced by subtracting a smooth background that solves Poisson's equation with boundary conditions set by the image's edges. Unlike the traditional windowed Fourier transforms, Periodic Plus Smooth Decomposition maintains sharp reciprocal lattice peaks from the image's entire field of view.