Applications of Compressive Sensing for EDS Analysis

Abstract

In a scanning/transmission electron microscopy (SEM/TEM) X-ray energy dispersive spectroscopy (EDS) experiment, limiting the radiation dose delivered to the sample is often extremely important. Recent developments in electron microscopy ^{1 2 3 4} have borrowed a technique from the mathematics community called compressive sensing (CS),⁵ which provides a mechanism for correctly inpainting missing data from highly undersampled (i.e. sparse) signals, subject to restrictions on how the signal is collected. In this study, a CS reconstruction algorithm developed for hyperspectral imagery known as Beta Process Factor Analysis (BPFA)⁶ was applied to EDS data collected on an SEM platform. The techniques are expected to be generalizable to STEM, as well as similar spectroscopic techniques, such as X-ray Fluorescence Spectrometry (XRF). Two-dimensional sparse EDS maps were acquired at a range of dwell times, and used as inputs for a CS-BPFA reconstruction. In the reconstructed data, the spectrum images are fully-featured and the elemental maps demonstrate signal-to-noise ratio (SNR) enhancements ranging from 17% to 300% depending on the X-ray line in question. Qualitatively, the interpretability of the maps is also significantly improved. These initial results indicate that BPFA CS reconstruction can successfully improve severely undersampled EDS maps, warranting added research in the quantitative effects of such a reconstruction. This technique would be relatively simple to extend to three dimensions, potentially expanding these benefits to FIB/SEM EDS tomography.

Slides

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