Reducing acquisition time and radiation damage: data-driven subsampling for spectro-microscopy

TL;DR

The paper addresses the challenge of long acquisition times and radiation dose in spectro-microscopy by developing data-driven sparse acquisition strategies. It introduces two schemes, RISS (Raster Importance Sampling for spectro-microscopy) and CURISS (CUR Importance Sampling for spectro-microscopy), which select energy levels and spatial rows using leverage-score–based importance measures and reconstruct missing data via matrix completion or CUR decomposition. The methods exploit the intrinsic low-rank structure of spectro-microscopy data to achieve accurate reconstructions with as little as 4-6% of measurements, demonstrated on iron oxide samples with and without spectral dictionaries. The work also proposes adaptive variants (ACURISS) with stopping criteria, showing robustness to spectral knowledge availability and highlighting potential for faster, dose-aware spectro-microscopy in materials science.

Abstract

Spectro-microscopy is an experimental technique which can be used to observe spatial variations in chemical state and changes in chemical state over time or under experimental conditions. As a result it has broad applications across areas such as energy materials, catalysis, environmental science and biological samples. However, the technique is often limited by factors such as long acquisition times and radiation damage. We present two measurement strategies that allow for significantly shorter experiment times and total doses applied. The strategies are based on taking only a small subset of all the measurements (e.g. sparse acquisition or subsampling), and then computationally reconstructing all unobserved measurements using mathematical techniques. The methods are data-driven, using spectral and spatial importance subsampling distributions to identify important measurements. As a result, taking as little as 4-6\% of the measurements is sufficient to capture the same information as in a conventional scan.

Figures (13)

• Figure 1: a) A schematic overview of a spectro-microscopy beamline (inspired by Hitchcock (2015). Monochromatic X-rays of a set energy are focused as the sample moves in a raster-like way. For full scans, the sample is scanned row-by-row as in b). One can reduce acquisition time and sample dose by only measuring a small subset of rows for each energy as in c).
• Figure 2: A matrix of exact rank $S$ (in this case $S=2$) can be represented using just $S$ of its columns and $S$ of its rows using the CUR decomposition. The only requirement is that the rows and columns are linearly independent.
• Figure 3: A graphical representation of random raster subsampling combined with the LoopedASD algorithm. Random raster sampling results in a dataset where the measurements correspond to blocks of entries for each row (left side). The LoopedASD algorithm aims to find two factors $\boldsymbol{X}$ and $\boldsymbol{Y}$ so that $\boldsymbol{XY}$ fits the observed measurements: $\mathcal{P}(\boldsymbol{D})\approx \mathcal{P}(\boldsymbol{XY})$.
• Figure 4: The amount of information retained with different subsampling strategies. The information measure is $(1 - \|\boldsymbol{D}-\boldsymbol{D}_{\mathrm{completed}}\|_F)/(1-\|\boldsymbol{D} - \boldsymbol{D}_{\mathrm{optimal}}\|_F)\cdot100\%$, where $\boldsymbol{D}_{\mathrm{completed}}$ is the completed dataset (with filled in entries) and $\boldsymbol{D}_{\mathrm{optimal}}$ is the best rank-$10$ approximation to $\boldsymbol{D}$ according to the Eckart-Young-Mirsky Theorem eckart1936approximation, i.e., truncated rank-$10$ singular value decomposition (SVD). The dataset is DS1 from townsend2022undersampling. For the raster sampling approaches, completion is done with LoopedASD, and the data shown is the average of 10 iterations. For the CUR sampling approaches, the CUR decomposition is the completion and the data shown is the average of 100 iterations.
• Figure 5: The spectral importance subsampling distribution (purple) for prior knowledge on the absorption spectra of three (potentially) present iron/iron-oxides. The incident energies (on the x-axis, in eV) where the most variance is explained are subsampled with higher probabilities.