Detecting small low emission radiating sources

Moritz Allmaras; David Darrow; Yulia Hristova; Guido Kanschat; Peter Kuchment

doi:10.3934/ipi.2013.7.47

Article Contents

2013, Volume 7, Issue 1: 47-79. Doi: 10.3934/ipi.2013.7.47

This issue Previous Article The attenuated magnetic ray transform on surfaces Next Article Bayesian inverse problems with Monte Carlo forward models

Detecting small low emission radiating sources

1.
Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81739 Munich
2.
The University of Texas Medical Branch, 301 UniversityBoulevard, Galveston, TX 77555
3.
Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, Minneapolis, MN 55455
4.
Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843

Received: January 31, 2012

Revised: April 30, 2012

Published: January 2013

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Abstract

In order to prevent influx of highly enriched nuclear material throu-gh border checkpoints, new advanced detection schemes need to be developed. Typical issues faced in this context are sources with very low emission against a dominating natural background radiation. Sources are expected to be small and shielded and hence cannot be detected from measurements of radiation levels alone. We consider collimated and Compton-type measurements and propose a detection method that relies on the geometric singularity of small sources to distinguish them from the more uniform background. The method is characterized by high sensitivity and specificity and allows for assigning confidence probabilities of detection. The validity of our approach can be justified using properties of related techniques from medical imaging. Results of numerical simulations are presented for collimated and Compton-type measurements. The 2D case is considered in detail.

Keywords:

Mathematics Subject Classification: Primary: 82D75, 35R30; Secondary: 81U40, 65N21.

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