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Inverse Problems and Imaging (IPI)
 

Detecting small low emission radiating sources

Pages: 47 - 79, Volume 7, Issue 1, February 2013      doi:10.3934/ipi.2013.7.47

 
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Moritz Allmaras - Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81739 Munich, Germany (email)
David Darrow - The University of Texas Medical Branch, 301 UniversityBoulevard, Galveston, TX 77555, United States (email)
Yulia Hristova - Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, Minneapolis, MN 55455, United States (email)
Guido Kanschat - Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843, United States (email)
Peter Kuchment - Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843, United States (email)

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:  Nuclear source detection, tomography, homeland security, Compton camera.
Mathematics Subject Classification:  Primary: 82D75, 35R30; Secondary: 81U40, 65N21.

Received: February 2012;      Revised: May 2012;      Available Online: February 2013.

 References