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REBEL: Convex Relaxations for Poisson GLRT

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Abstract

This paper proposes an adaptive method for detection of sparse signals generated from a Poisson distribution, motivated by the problem of preventing nuclear fuel from crossing secure borders. The procedure, termed REBEL, is based on a convex relaxation of a generalized likelihood ratio test (GLRT). The relaxed problem is solved using iterative methods. In the case of 1-sparse signals, the proposed algorithm is shown to be optimal in terms of minimizing the false positive and false negative rates as the sample size grows.

Citation

Z. T. Harmany, M. L. Malloy, A. Bhargava, N. Rao and S. J. Wright, “REBEL: Convex relaxations for Poisson GLRT”, in (submitted to) IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013.

BibTeX

@inproceedings{harmany-icassp2013-rebel,
  title = {REBEL: Convex relaxations for Poisson GLRT},
  author = {Harmany, Zachary T. and Malloy, Matthew L. and Bhargava, Aniruddha and Rao, Nikhil and Wright, Stephen J.},
  booktitle = {(submitted to) IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  year = {2013},
  abstract = {This paper proposes an adaptive method for detection of sparse signals generated from a Poisson distribution, motivated by the problem of preventing nuclear fuel from crossing secure borders.  The procedure, termed REBEL, is based on a convex relaxation of a generalized likelihood ratio test (GLRT). The relaxed problem is solved using iterative methods.  In the case of 1-sparse signals, the proposed algorithm is shown to be optimal in terms of minimizing the false positive and false negative rates as the sample size grows.}
}