Suppressing Background Radiation Using Poisson Principal Component Analysis

Suppressing Bac kground Radiation Using P oisson Principal Comp onen t Analysis P . T andon ∗ , P . Huggins ∗ , A. Dubra wski ∗ , S. Lab o v ∗∗ , K. Nelson ∗∗ ∗ Auton Lab, Carnegie Mellon Univ ersity ∗∗ La wrence Livermore National Laboratory In tro duction. Performance of n uclear threat detection systems based on gamma-ray sp ectrometry often strongly dep ends on the abilit y to identify the part of measured signal that can b e attributed to background radiation. W e ha ve successfully applied a metho d based on Principal Component Analysis (PCA) to obtain a compact null-space mo del of bac kground sp ectra using PCA pro jection residuals to derive a source detection score. W e hav e shown the metho d’s utility in a threat detection system using mobile sp ectrometers in urban scenes (T andon et al 2012). While it is commonly assumed that measured photon counts follow a P oisson pro cess, standard PCA makes a Gaussian assumption ab out the data distribution, whic h may b e a p o or approximation when photon counts are lo w. This pap er studies whether and in what conditions PCA with a Poisson-based loss function (Poisson PCA) can outp erform standard Gaussian PCA in mo deling bac kground radiation to enable more sensitive and sp ecific n uclear threat detection. Preliminaries. Radiation measurements are non-negativ e integer v ectors which are photon counts across subse- quen t energy bins. In our case there are 128 bins. Figure 1A sho ws an example measuremen t where photon coun ts are low in high energy bins. Figure 1B sho ws an example of one of these bins. W e can see that a Poisson mo del of the data b etter matches the true distribution than a Gaussian mo del. Standard PCA pro jection is optimal at explaining v ariance assuming the data is Gaussian. Collins et al. 2002 provides a generalization of PCA to a range of loss functions in the exp onen tial family which they term E-PCA. One v arian t utilizes a P oisson error mo del, a form ulation which w e adopt in our study . Exp erimen ts. Our radiation data is collected in a cit y b y a v ehicle carrying a double 4x16 NaI planar scintillator, with measuremen ts taken ov er in terv als of ab out 1s eac h. Three metho ds for bac kground mo deling are compared: standard (Gaussian) PCA, Poisson PCA, and a Gaussian PCA-based sp ectral anomaly detector currently fielded in our source detection system. All metho ds were trained on a set of roughly 1,000 background radiation measure- men ts. Tw ent y testing data sets w ere created. Eac h consisted of roughly 1,000 bac kground (negative) data p oints and also the same n umber of synthetic p ositiv e p oin ts created b y injecting the negative p oin ts with additional coun ts due to a hypothetical synthesized fissle materials source. There is one testing data set for each distance to source in interv als of 1m, from 1 to 20m. Eac h of the ev aluated metho ds estimated background mo dels using training data and pro duced a reconstruction error score for each data p oint in the test sets. A successful metho d will distinguish p ositiv e from negative data p oints. W e measured Symmetric Kullbac k- Leibler Div ergence (SKL) b et w een the distributions of scores for negativ e and p ositiv e test data in eac h testing data set. A histogram estimator w as used to compute SKL. Figures 2A-D plot the results for different num b ers of principal comp onen ts used b y each metho d, from 2 to 5. Since the pro jection obtained b y Poisson PCA may v ary somewhat dep ending on the initial starting p oin t of the optimization, 30 exp eriments were run for each num b er of principal comp onen ts, and [0 . 20 , 0 . 80] confidence in terv als were dra wn. (a) Sample Radiation Reading (b) Mo del Comparison Figure 1: Comparing Poisson Mo del vs. Gaussian Mo del of radiation measurements 1 (a) N=2 PCs (b) N=3 PCs (c) N=4 PCs (d) N=5 PCs (e) Max SKL P erformance Figure 2: SKL p erformance of Gaussian PCA, P oisson PCA, and our existing Sp ectral Metho d Figure 2E plots the top SKL p erformance at each distance (1-20m). F or each metho d and distance to source, the best SKL score is rep orted b y c ho osing the optimal n umber of principal comp onen ts ranging from 1 to 5. When the sensor is near the source, all metho ds can distinguish background from source-injected data very w ell. P oisson PCA, ho wev er, outp erforms other metho ds at large distances (low er source injection counts), suggesting Poisson PCA ma y impro v e source detection times for mo ving sensors. It ma y also benefit detection with shorter observ ation time in terv als, p oten tially improving p eak signal-to-noise ratios for measurements tak en along a tra jectory . W e note that our findings matc h the intuition that at large distances there will b e low er measured counts of source- originating photons, so Gaussian appro ximations of unexplained v ariance will b ecome less accurate. Discussion and Conclusions. Detecting faint sources among noisy background is an imp ortant practical prob- lem, and our results suggest that P oisson PCA can bo ost source detection p o wer at large distances, and potentially reduce source detection times for mobile sensors. Interestingly , the more standard PCA metho ds tend to p erform b etter at close range, suggesting that the optimal mo del may b e an ensemble of differen t metho ds. References. Mic hael Collins, Sanjo y Dasgupta, and Robert Schapire. A generalization of principal comp onen ts analysis to the exp onen tial family . In T. G. Dietteric h, S. Bec ker, and Z. Ghahramani, editors, Adv ances in Neural Information Pro cessing Systems 14 (NIPS), Cambridge, MA, 2002. MIT Press. Prateek T andon, Peter Huggins, Artur Dubrawski, Jeff Schneider, Simon Lab ov and Karl Nelson. Source lo cation via Ba yesian aggregation of evidence with mobile sensor data. (under review). This work has b een supp orted by the US Department of Homeland Security , Domestic Nuclear Detection Office, under comp etitiv ely a warded 2010-DN-077-ARI040-02. This supp ort do es not constitute an express or implied endorsement on the part of the Go vernmen t. La wrence Liv ermore National Laboratory is op erated by Lawrence Liv ermore National Securit y , LLC, for the U.S. Departmen t of Energy , National Nuclear Securit y Administration under Contract DE-AC52-07NA27344. 2