A Geometric Approach to Spectral Analysis

TL;DR

This paper introduces a geometric framework for spectral analysis that addresses limitations of traditional methods, enabling the identification of missing spectral components and their properties in gamma-ray spectra.

Contribution

It presents a novel geometric approach to spectral analysis, overcoming issues with linearity assumptions and missing libraries in gamma-ray spectrum decomposition.

Findings

Successfully identified missing spectral components in simulated data

Validated the geometric approach on Monte Carlo-generated spectra

Provided solutions for locating photopeaks and estimating fractions

Abstract

Analyses of gamma-ray spectra, acquired through non-invasive techniques, have found applications in fields such as medicine, industry and homeland security. Constituent gamma-ray spectra of a chemical compound have been determined from its sole spectrum through a forward Monte Carlo simulation coupled with a least squares method (MCLLS). The method's limitations include its linearity assumption and its oversensitivity to correlated or noisy data, which render the method unfit to deal with such numerical ill conditioning. Recently this issue was tackled by iteratively reducing the condition number of the linear system of equations. Despite its superior results, it is not suitable for cases where there are missing libraries in the analysis. Our work introduces a novel framework that allows treating spectral analyses problems through geometrical insights. Based on this it was possible to propose solutions to three problems regarding the missing library: to find its photopeak, its most probable fraction, and an envelope around its spectrum. We successfully validated these on some Monte Carlo-generated radionuclide gamma-ray spectra.