Asymptotic Source Detection Performance of Gamma-Ray Imaging Systems Under Model Mismatch

Asymptotic Source Detection Performance of Gamma-Ray Imaging Systems Under Model Mismatch,10.1109/TSP.2011.2162326,IEEE Transactions on Signal Process

Asymptotic Source Detection Performance of Gamma-Ray Imaging Systems Under Model Mismatch   (Citations: 1)
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Likelihood-based test statistics for the task of de- tecting a radioactive source in background using a gamma-ray imaging system often have intractable distributions. This compli- cates the tasks of predicting detection performance and setting thresholds that ensure desired false-alarm rates. Asymptotic distributions of test statistics can aid in predicting performance and in setting detection thresholds. However, in applications with complex sensors, like gamma-ray imaging, often only ap- proximate statistical models for the measurements are available. Standard asymptotic approximations can yield inaccurate per- formance predictions when based on misspecified models. This paper considers asymptotic properties of detection tests based on maximum likelihood (ML) estimates under model mismatch, i.e., when the statistical model used for detection differs from the true distribution. We provide general expressions for the asymptotic distribution of likelihood-based test statistics when the number of measurements is Poisson, and expressions specific to gamma-ray source detection that one can evaluate using a modest amount of data from a real system or Monte Carlo simulation. Considering a simulated Compton imaging system, we show that the proposed expressions yield more accurate detection performance predic- tions than previousexpressions that ignore modelmismatch.These expressions require less data and computation than conventional empirical methods.
Journal: IEEE Transactions on Signal Processing - TSP , vol. 59, no. 11, pp. 5141-5151, 2011
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    • ...We apply the methodology of [5] to compute the detection performance in terms of ROC with an asymptotic approximation that accounts for model mismatch...
    • ...Under suitable conditions, ˜ �� is the limit of the sequence of estimates ˜ �� �� as �� →∞ . One possible set of regularity conditions that guarantees existence, uniqueness, and convergence is given in [5]...
    • ...The convergence of the QMLE is stated in Theorem 1, which extends Theorem 2.2 of [8] to the case of a Poisson number of measurements. The proof is given in [5]...

    Daniel J. Lingenfelteret al. Predicting ROC curves for source detection under model mismatch

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