Variance Preserving Spectral Subsampling

Hansen, Hyrum J. and Burr, Thomas L. and Croft, Stephen and Kirkpatrick, John and Mercer, David J. and Sagadevan, Athena A. and Stockman, Tom J. and Stark, Emily N. (2025) Variance Preserving Spectral Subsampling. Algorithms, 19 (1): 25. ISSN 1999-4893

Abstract

Generating statistically faithful short-duration gamma-ray spectra from a single long measurement is essential in nuclear safeguards, supporting tasks such as algorithm development and machine-learning applications, especially when list-mode data are unavailable. Existing subsampling methods often distort the statistical characteristics of genuine short-duration measurements, leading to biased or unreliable analytical outcomes and thereby undermining downstream tasks. In this work, we compare five subsampling approaches using a benchmark set of 156 genuine replicate spectra collected with a high-purity germanium detector. We evaluate each method with respect to run-to-run variance, channel-to-channel variance, and preservation of total counts (losslessness). Across a wide range of subsampling ratios, only binomial subsampling without replacement consistently reproduces the statistical properties of genuine short-duration spectra, maintaining proper dispersion even in sparse spectral regions and perfectly preserving total counts. These results provide a mathematically principled and practically validated framework for generating synthetically shortened spectra when true short-duration measurements are unavailable.