An EM approach to mineral analysis using natural gamma rays

  • Authors:

  • Bill Moran;Du Q. Huynh;Xuezhi Wang;Michael Edwards;Andrew Harris;Barbara F. La Scala

  • Affiliations:

  • Department of Electrical and Electronic Engineering, The University of Melbourne, Australia;School of Computer Science and Software Engineering, The University of Western Australia, Australia;Department of Electrical and Electronic Engineering, The University of Melbourne, Australia;Scantech, Camden Park, SA 5038, Australia;Scantech, Camden Park, SA 5038, Australia;Department of Electrical and Electronic Engineering, The University of Melbourne, Australia

  • Venue:
  • Digital Signal Processing
  • Year:
  • 2009

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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 Cramer-Rao lower bounds for the estimators are calculated.