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Intensity and Dictionary Estimation for Nuclear Spectroscopy Using a Sparse Double Optimization
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DOI：10.1109/tim.2026.3709451.png)
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Abstract
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Gamma-ray spectrometry at low count rates--- common in nuclear security screening, short-duration field measurements, and environmental assay—demands robust extraction of pulse parameters from noisy time-domain traces. Existing approaches either use fixed pulse templates that introduce bias when the detector response is imperfectly known, or employ data-driven models that sacrifice physical interpretability. We bridge this gap with sparse double optimization (SDO), a likelihood-based framework that jointly estimates pulse occurrences, energies, a parametric dictionary, and Poisson detection rate from raw traces via alternating proximal-gradient optimization. On a low-rate toy benchmark, SDO achieves precision/recall <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.56/1.00$ </tex-math></inline-formula> (RMSE 0.031), far exceeding fixed-dictionary baselines (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.03/0.50$ </tex-math></inline-formula>). On surrogate 137Cs data, aggregated multiwindow metrics (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10 \times 0.5$ </tex-math></inline-formula> s windows) yield precision <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.802~\pm ~0.031$ </tex-math></inline-formula>, recall <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.681~\pm ~0.040$ </tex-math></inline-formula>, and the smallest photopeak centroid bias (−6.0 keV) among the five methods compared, while fixed-template baselines with a matched dictionary (e.g., Lasso/ISTA) achieve higher precision and recall on this surrogate where the true pulse shape is known. Calibration-based activity estimation achieves 2.5 % point-estimate error with a calibration-dominated 95 % CI of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\approx }\pm 54{\,}\%$ </tex-math></inline-formula>, narrowing to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\approx }\pm 14{\,}\%$ </tex-math></inline-formula> with a 5 s calibration and a 5 s evaluation window. A preliminary validation on a real charge-sensitive preamplifier trace (10 MHz, 60 s) yields postmerge detection rates consistent with matched-filter and threshold baselines, suggesting applicability beyond surrogate data.
Keywords:
Dictionary learning
nuclear spectroscopy
Poisson process
proximal gradient
sparse regression
Journal
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5.9
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1.9W
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5.8W