An EM approach to mineral analysis using natural gamma rays

B. Moran; Du Huynh; X. Wang; M. Edwards; A. Harris; B.F. La Scala

doi:10.1016/j.dsp.2009.04.001

An EM approach to mineral analysis using natural gamma rays

B. Moran, Du Huynh, X. Wang, M. Edwards, A. Harris, B.F. La Scala

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Abstract

We describe here a method for the analysis of materials on a conveyor belt using the natural gamma spectra collected with a BGO (Bismuth Germanate) gamma ray detector. This detector collects gamma ray emissions from the Potassium (K), Uranium (U), and Thorium (Th) atoms in the materials. Based on these data, and using a Poisson model for the data generation, a statistical model is proposed and an approximate maximum likelihood (ML) technique based on the expectation-maximization (EM) algorithm is then used to estimate the amount of each of the three elements in the material. The statistical model is further refined to incorporate parameters of drift in the detector and an estimation technique for this is developed and tested against real data. The Cramér–Rao lower bounds for the estimators are calculated.

Original language	English
Pages (from-to)	793-808
Journal	Digital Signal Processing
Volume	19
Issue number	5
DOIs	https://doi.org/10.1016/j.dsp.2009.04.001
Publication status	Published - 2009

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Moran, B., Huynh, D., Wang, X., Edwards, M., Harris, A., & La Scala, B. F. (2009). An EM approach to mineral analysis using natural gamma rays. Digital Signal Processing, 19(5), 793-808. https://doi.org/10.1016/j.dsp.2009.04.001

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abstract = "We describe here a method for the analysis of materials on a conveyor belt using the natural gamma spectra collected with a BGO (Bismuth Germanate) gamma ray detector. This detector collects gamma ray emissions from the Potassium (K), Uranium (U), and Thorium (Th) atoms in the materials. Based on these data, and using a Poisson model for the data generation, a statistical model is proposed and an approximate maximum likelihood (ML) technique based on the expectation-maximization (EM) algorithm is then used to estimate the amount of each of the three elements in the material. The statistical model is further refined to incorporate parameters of drift in the detector and an estimation technique for this is developed and tested against real data. The Cram{\'e}r–Rao lower bounds for the estimators are calculated.",

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AU - Harris, A.

AU - La Scala, B.F.

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AB - We describe here a method for the analysis of materials on a conveyor belt using the natural gamma spectra collected with a BGO (Bismuth Germanate) gamma ray detector. This detector collects gamma ray emissions from the Potassium (K), Uranium (U), and Thorium (Th) atoms in the materials. Based on these data, and using a Poisson model for the data generation, a statistical model is proposed and an approximate maximum likelihood (ML) technique based on the expectation-maximization (EM) algorithm is then used to estimate the amount of each of the three elements in the material. The statistical model is further refined to incorporate parameters of drift in the detector and an estimation technique for this is developed and tested against real data. The Cramér–Rao lower bounds for the estimators are calculated.

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10.1016/j.dsp.2009.04.001