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Poisson Modeling and Bayesian Estimation of Low
Photon Count Signal and Noise Components
Prateek Tandon∗, Peter Huggins∗, Artur Dubrawski∗, Karl Nelson†and Simon Labov†
∗Auton Lab, Robotics Institute
Carnegie Mellon University
Pittsburgh, PA 15213
†Lawrence Livermore National Laboratory
Livermore, CA 94550
Abstract—Mobile radiation detectors aim to help identify
sources of radiation. Finding a radioactive source in a man-made
environment such as a city can be challenging because the additive
signal received by the detector contains both photon counts from
the source of interest and from the cluttered and variable ambient
background. Decomposing the overall radiation spectrum into its
background and source signal components is key. When either or
both of the background or source components is low in photon
counts, the estimation of signal components can become especially
challenging.
Gamma-ray spectrometry data is typically presumed to be
created with a Poisson process, though Gaussian-based estimators
are typically used to approximate the truly Poisson-distributed
data. Generally this approximation suffices, but performance loss
can occur when photon counts affecting a sensor are low in
number for any signal component. Low photon count signal
and/or noise components can occur in a variety of real world
scenarios. Photon counts from the source may be low because
the source is very weak or only observable from large standoff
distances. Photon count rate from both source and background
may be low if small sensors (with limited surface area) are used
or if measurement time is limited.
Our study experiments with augmenting established anomaly
detection and match filter signal component estimators with
Poisson-based models. We apply estimators such as the Poisson
Principal Component Analysis (Poisson PCA) and the Zero-
Inflated Poisson (ZIP) models to the source detection problem and
benchmark with respect to popular estimators in the literature.
Finally, we apply Bayesian Aggregation to the Poisson-based esti-
mators to aggregate evidence across multiple spatially-correlated
sensor observations. Our results indicate that the use of such
techniques can aid threat detection when photon counts are low
in signal and/or background noise components.
I. INTRODUCTION
Mobile radiation detectors aim to help law enforcement
effectively identify sources of potentially harmful radiation.
Photons emitted from radioactive sources in the environment
can be measured by radiation spectrometers. Radiation spectra
are denoted as the histogram of counts of photons hitting a
sensor at a set of chosen discrete energy ranges for a particular
measurement time interval. Because various threatening radi-
ation sources have characteristic physical peaks at particular
energy levels, mobile spectrometer systems aim to help quickly
map and characterize possible radiation threat.
The complicated, variable radiation landscapes of most ur-
ban scenes (such as major cities) can, however, make detecting
a radiation source quite challenging. A radiation source being
searched for can be a needle in the haystack of cluttered
background radiation emanated from typical benign radioac-
tive sources present in many urban scenes. Developed threat
detection algorithms are expected to accurately distinguish
threats from non-threats, even when photon count rates from
the source and/or background may be low and possibly limited
in intrinsic information.
The problem of Low Photon Count Signal and Noise
Component Estimation is to succeed in detecting a radioactive
source even when the effective photon count rate received by
a sensor is especially low for either the background or source
components. The low photon count rate scenario may occur
for a variety of reasons due to properties of the source and/or
of the sensor(s) used.
An important class of cases is where the photon count
rate from the source may be low relative to the background,
making estimation of source counts difficult. The radioactive
source being searched for may be very weak, occluded by
signal-attenuating obstacles (e.g. be inside a building), or be
observable only far away in standoff distance from the sensor.
If the source is deliberately engineered to be shielded, it may
be directionally attenuated, leading a loss in photon counts
detected by the sensor. In this class of cases, the photon counts
in the source component are expected to be low, though the
background count rate may be as usual.
Another set of cases is where the photon count rate from
both background and source are low. This can occur due
to limitations of the sensor data collection process and/or
hardware. For instance, a sensor may only have been able to
briefly survey an area, collecting only a handful of photon
counts from both background and source due to lack of data
collection time. Additionally, sensors may also be limited
in their intrinsic material detection capability and sensitivity.
Sensors can vary in size, shape, and materials which affects
their detection capabilities. Smaller sensors can be more cost-
effective to deploy, but they will receive fewer counts from
both the background and the source than larger sensors due to
their smaller surface area.
In all of these cases, the constraint of fewer photon counts
in radiation spectra makes the detection problem harder. Fewer
photon counts in either a source or background component
generally means that each component is harder to estimate.
An algorithm has less data to reason about the delimitation of
signal components and is subject to greater possible estimation
error. The goal is to develop algorithms that can extract the
most useful information possible out of available photon count
sensor data to succeed in detecting the source.
A. Background Estimation
A radiation spectrum is the histogram of counts of photons
observed at a set of energy levels. Radiation spectra are often
presumed to be composed of two major components: the signal
due to the radioactive source of interest (if any) and the
contribution of characteristic background radiation variation
in the scene. In searching for the presence of source signal in
a spectrum, one of the first steps is to perform Background
Estimation on the spectrum.
Background estimators are statistical estimators that seek
to estimate the number of photon counts due to background
(B) and the number of photon counts due to the source (S).
By estimating these two quantities, a background estimator can
thus calculate its estimate of the Signal-To-Noise Ratio (SNR)
of the spectrum as:
SN R =S
√B(1)
When forming the SNR score, the noise term is given by
√B(the square root of total background photon counts) as
opposed to B(total background photon counts) since radiation
data is presumed Poisson where the mean is proportional to
the variance.
Anomaly detectors and match filters are two approaches to
background estimation commonly used in practice. The goal
of anomaly detection is to flag spectra that are distinct from
typical background. Anomaly detection typically assumes no
knowledge of a source template and simply uses a model
of expected background to measure the background (typical
variation) and source (unusual deviation) components of a
measurement. Match filtering, in contrast, allows the user
to specify a specific source template of interest to match
against spectrum observations. Both methods allow estimation
of background and source components.
Principal Components Analysis (PCA) is a common tech-
nique of anomaly detection to learn a model for typical
background data. When PCA is run on background radiation
data, it builds a shape model for what typical background
should look like. Additionally, the top principal components
of the model capture the typical background variation of the
data. When new radiation observations are projected onto the
PCA basis learned from training data, the reconstruction error
corresponds to anomalous behavior from typical background
– behavior that is likely to be due to the source. For our
experiments, we retain the top five components since these
have been empirically shown to capture the principal modes
of variation in the data [1].
The Spectral Anomaly Detector [1] is a variant of PCA that
learns the PCA background model from the correlation matrix
of the background data rather than the covariance. This helps
avoid overly biasing the PCA model towards the most common
background energies. In addition, the resulting compressed
space is used as the null-space model, capturing the expected
types of variability in the background in the top few prin-
cipal components. Like vanilla PCA, the reconstruction error
indicates possible source signal. However, the sum of squared
residuals after background subtraction is normalized by the
sum of measurement counts to form an SNR-like “Spectral”
score.
Match filtering, unlike anomaly detection, assumes knowl-
edge of a source template currently being searched. The
method allows defining of a source-specific window in the
energy space of the spectrum where source photon counts
are maximally likely to appear. Energy Windowing Regression
[2] is a common technique for match filtering. A regression
estimator is then trained to predict, for a new radiation vector,
the amount of background in the window from the background
photon counts outside the window. Counts left over in each bin
are likely to be related to source signal. Often times, the Least
Squares Estimator (i.e. Linear Regression) is used to facilitate
the prediction. The model typically used is given by:
ˆ
B(y) = (XTX)−1XTy(2)
where Xis the matrix of predictor energy bins and y
is the sum of background counts in the source window.
The ˆ
Bestimator, after training, predicts, for a new radiation
spectrum, how many background counts are estimated in the
source window given the photon counts present outside of the
source window. The remainder is assumed to be the source
signal. Energy Windowing Regression can significantly boost
detection when the expected source type is known [2].
B. Poisson Modeling
Spectrometry data is often presumed to be created with
a Poisson Process. However, the available anomaly detection
and match filtering methods typically rely on Gaussian models
of the data. In anomaly detection, both the vanilla PCA
and Spectral Anomaly Detector methods assume a Gaussian
distribution of the data and primarily find linear directions of
maximal variance. Likewise, Energy Windowing Regression is
typically based on a Linear Regression (also Gaussian) model
of the data.
When the photon count rate for both source and back-
ground components is sufficiently high, a Poisson distribu-
tion can be approximated well by a Gaussian distribution.
In these cases, the Gaussian modeling assumption does not
invoke much loss. When the photon count rate for either or
both components is low, however, the Gaussian approximation
ceases to work as a sufficient model of the data.
The remedy is to augment the estimation process with
Poisson models to boost performance. Our study experiments
with using Poisson Principal Component Analysis (Poisson
PCA) [3] instead of standard Gaussian PCA to estimate source
SNR using anomaly detection. Similarly, we experiment with
using Zero-Inflated Poisson (ZIP) Regression [4] instead of
Linear (Gaussian) Regression when estimating SNR with a
match filter. Our results suggest that these Poisson-based
methods can mine additional useful information from the data,
unavailable in a pure Gaussian model, to help detect potentially
harmful sources of radiation.
In addition, we use our Bayesian Aggregation (BA) algo-
rithm to further improve detection performance. BA leverages
spatial aggregation of multiple correlated radiation observa-
tions to robustly test source location hypotheses [5]. By
aggregating evidence statistically over multiple observations,
detection performance is made more robust against possible
spurious noise in the data that can cause false alarm.
II. ME TH OD S
A. Data and Point Source Simulator
Our experiment data set contains real field data collected
over a period of five consecutive days using a double 4x16”
NaI planar spectrometer installed on a van driving in an urban
area. The data contains 70,000 measurements, reflective of
background and any existing nuisance sources, collected at 2
second intervals while the vehicle was in motion. Annotation
data recorded for each measurement include timestamp, lon-
gitude and latitude obtained from GPS, and the current speed
of the vehicle.
The radiation spectra in the data are 128-dimensional
vectors of counts of particles hitting the sensor where each
dimension corresponds to a specific energy interval. Each
spectrum is a histogram of counts at 128 energy intervals,
quadratically spaced across the 80 keV to 2800 keV energy
range. The data can be down-sampled to simulate different
background count rates, including relatively low ones.
A source simulator is used to inject user-supplied synthetic
radiation profiles into collected background radiation data to
simulate the presence of point sources. Given a geographic
subregion, the simulator chooses a random location within
proximity to the collected trajectory, and injects additional
source photon counts to the pre-existing background measure-
ments according to a Poisson distribution. In injecting the
source, the simulator takes into account the expected exposure
of the source to the sensor, the velocity of the mobile detector,
and the duration of the measurement interval. The simulator
also allows specification of source type and source intensity
(e.g. count rate).
B. Poisson PCA
Poisson PCA is an extension of PCA that allows a Poisson-
type loss function instead of the sum of squared error loss
function used by traditional PCA [3]. The sum of squared error
loss function in traditional PCA imposes a Gaussian model
on the data. Poisson PCA uses a Poisson-based loss function
instead.
Standard PCA finds key linear directions of variation in
the data and allows for negative components. Poisson PCA,
in contrast, gives a space of typical background spectra which
are always non-negative. Accumulations of measurement de-
viations in unlikely energy bins are much less likely to be
over-fitted. We use the Poisson PCA formulation in [6] for
our experiments.
C. Zero-Inflated Regression Poisson Match Filter
The standard Energy Windowing Regression match filter
uses the Least Squares Estimator to derive source and back-
ground components, imposing a Linear (Gaussian) Regression
model on the data. One can use a Poisson Regression model
for the expectation instead:
E(y|x) = eλTx(3)
where yis the predicted sum of counts in the energy
window, xis counts in the predictor energy bins, and λis
the Poisson mean. Using Poisson Regression instead of Linear
Regression in match filtering can help improve the model.
One hurdle is that extremely low photon count data can also
be sparse and contain excess zeros that occur by chance in no
signal cases. These excess zeros, if not accounted for, may
lead to over-dispersion in the estimates of the λparameters in
the Poisson model when signal is expected. Since the mean
and variance are given by the same parameter in a Poisson
distribution, fitting a Poisson distribution to data with very
sparse number of counts may not lead to a good model of
the data. An effective numerical trick is to use a Zero-Inflated
Poisson (ZIP) model:
P(yj= 0) = π+ (1 −π)e−λ(4a)
P(yj=hi) = (1 −π)λhie−λ
hi!, hi≥1(4b)
The ZIP model on the radiation data uses a two-step
hierarchal approach. Logistic regression is used to first classify
the presence of non-zero counts from predictor energy bins.
If the spectrum is predicted to have non-zero background
counts in the source window, then Poisson Regression is run
to predict the amount. The separate probability densities for
the zero count and non-zero count cases help prevent over-
dispersion when estimating the mean parameter of the Poisson
distribution for the case of expected non-zero source signal.
III. EXP ER IM EN TS A ND DISCUSSION
Our experiments consist of benchmarking different
anomaly detection methods with respect to each other as well
as comparing different match filter methods. Match filters typ-
ically outperform anomaly detectors when the expected source
type is known. In all of our experiments, we compare methods
mostly using a single shielded fissile material source type. It is
generally established that anomaly detectors will outperform
match filters when a particular source type is expected [5].
Thus, this comparison was not particularly interesting and is
omitted. There are, however, interesting significant differences
that emerge internally within the category of anomaly detection
methods and internally within the category of match filter
methods.
A. Benchmarking Poisson PCA vs. Gaussian PCA
We benchmarked the detection capability of Poisson PCA
with respect to other anomaly detectors in the literature such
as the vanilla Gaussian PCA and Spectral Anomaly Detector
methods. A training set of 13,278 un-injected background
measurements was subsampled from our urban data set. All
methods built null models for the training data, storing their
top Nprincipal components.
A testing set of 13,015 background spectra was subsampled
from the data. The un-injected data was used as a negative
example set. The point source simulator was used to inject
synthetic point sources into the testing data to form a posi-
tive example set containing source-injected measurements at
different distances to the source, from 1to 20m.
All methods assigned scores to all positive and negative
examples based on their learned models from training. Distri-
butions of positive and negative scores were assembled, and
discriminative capability was compared between methods. The
key success metric used was the Symmetric Kullback-Leibler
(SKL) divergence between positive and negative point score
distributions:
KL(P||Q) = X
i
P(i) ln P(i)
Q(i)(5a)
SK L(P||Q) = 1
2[KL(P||Q) + K L(Q||P)] (5b)
where Pindicates the distribution of positive scores and
Qindicates the distribution of negative scores for a partic-
ular method. Typically, KL divergence can be used to non-
parametrically compare distributions. Standard KL divergence,
however, is not symmetric, so the definition of the SKL
divergence helps to fix this.
The SKL formula estimates the difference (average log-
odds ratio) between two distributions. A higher SKL indicates
that the distribution of positive scores is increasingly distinct
from the negative score distribution, and thus source is more
detectable against background. The top-performing method for
the low count detection problem should produce the greatest
divergence between the positive and negative score distribu-
tions.
1) Detecting a far away source: An experiment was set up
that allocated each anomaly detection method some number,
from N= 2 to 5of their top Principal Components (PCs), and
the SKL performance was compared at each distance (from
1-20m) to a source. Figures 1(a)-1(d) compare the Gaussian
PCA, Spectral Anomaly Detector, and Poisson PCA methods
for different numbers of PCs. Figure 1(e) shows the maximum
SKL performance plotted over the best combination of PCs at
each distance for each method.
The experiment dealt with the case of low photon count rate
from the source but normal background photon count rates.
The source count rate was 65 counts/sec at 10m standoff from
the source, while the background count rate was 1263 ±267
counts/sec. The source is thus well within the tolerance of the
background, though the background rate is not considered low.
The SKL metric peaks near the source for all methods as
all methods succeed in close-range detection. It falls off for
all methods as standoff distance is increased to the source,
but falls off slower for Poisson PCA. The results suggest that
Poisson PCA outperforms other methods in detecting far away
sources at distances where source-originating photon counts
are very low.
(a) N=2
(b) N=3
(c) N=4
(d) N=5
(e) Max SKL
Fig. 1. SKL comparison of methods as a function of distance to the source.
(a) N=2
(b) N=3
(c) N=4
(d) N=5
(e) Max SKL
Fig. 2. SKL comparison of methods when detecting a faint source.
2) Detecting a faint source: The experiment was repeated
with a weaker source (i.e. lowered count rate) injected into the
background data. For this experiment, the overall counts from
the source were scaled down by half from the first experiment.
The source count rate was 33 counts/sec at 10m standoff, and
the background count rate remained unchanged.
The results indicate that Poisson PCA outperforms other
methods in detecting low intensity sources that have half
the photon counts from the source intensity used in the first
experiment. Interestingly, there is even more possible utility to
Poisson PCA for detecting sources at large standoff distances
to the sensor. As can be seen in Figure 2(e), the performance
gain from Poisson PCA comes much earlier on the distance
scale than it did in the first experiment. In the first experiment
we saw Poisson PCA outperform Gaussian methods at about
13m standoff to the source, while with the lowered intensity,
the performance gain can come at even 9m standoff from the
fainter source. More benefit manifests in the top four and five
principal components (Figures 2(c)-2(d)).
3) Detecting a source with shorter livetime: We also
performed an experiment where measurements had reduced
sensor livetime. The counts in the measurement (for both
background and source) were scaled to simulate halved sensor
measurement intervals. Figure 3(a) shows the maximum SKL
performance. The results indicate that Poisson PCA can help
detect sources at shorter measurement interval. The net effect
is that sensors can travel faster, covering more area while still
providing useful levels of source detection.
(a) Max SKL
Fig. 3. SKL comparison of methods when detecting a source with shorter
measurement livetime.
B. Benchmarking Poisson Match Filters vs. Gaussian Match
Filters
An experiment was designed to test different match filter
background estimators in their capability to estimate source
and background counts from spectra that were low in both
background and source counts. The average background count
rate was reduced to only 22 counts/sec with the source count
rate being even less, making it a very challenging detection
scenario.
We compared three different match filters: the vanilla
Linear (Gaussian) estimator, a Poisson regression method, and
the Zero-Inflated Poisson (ZIP) method. Each estimator was
trained on a set of 1,527 radiation observations consisting
of background radiation to match against a shielded fissile
materials source template. The estimators were subsequently
(a) Source Component Estimation Error
(b) Background Component Estimation Error
(c) SNR Estimation Error
(d) Signed Error
(e) Weighted Mean Method
Fig. 4. Experiments comparing match filter estimators.
tested on a set of 23,389 radiation background observations
with source-injected counts at a range of different distances
and exposures to a point source. Each estimator estimated
the background and source count amounts in each of the
observations, and the errors were plotted.
Figures 4(a)-4(b) show mean absolute error in estimation
of source and background photon counts for each method.
Poisson Regression has a slight gain over standard Linear
(Gaussian) Regression, while ZIP Regression has a major
advantage in the match filter. Figure 4(c) shows mean absolute
error in estimation of Signal-to-Noise Ratio (SNR). Both
Poisson and ZIP Regression outperform Linear (Gaussian)
Regression in reducing SNR estimation error.
Interestingly, the Gaussian and ZIP Regression Match Filter
estimation errors were only weakly correlated. The background
estimation errors exhibited a linear correlation value of only
0.5519, while the SNR estimation errors exhibited only a
0.2745 linear correlation value. This indicates that the two
methods are extracting different information from spectra to
flag sources.
Figure 4(d) plots the signed error of the Gaussian and
ZIP models. The direction of the signed error is opposite.
Gaussian models tend to systematically overestimate back-
ground components while ZIP models systematically appear
to overestimate the source component. Using this observation,
we created a mixed method that would fuse the Gaussian and
ZIP component estimates in a Weighted Mean. The idea was
to regress the Gaussian and ZIP components against the true
amounts to attempt to cancel out signed estimation error as
much as possible. This method had some success in lowering
the SNR estimation error even further as shown in Figure 4(e).
C. Incorporation into BA Framework
To further boost performance detection for these challeng-
ing signal estimation problems, we leveraged the Bayesian
Aggregation (BA) algorithm [5]. BA is a framework for
spatially aggregating multiple noisy, low Signal-to-Noise Ratio
(SNR) observations to score a geographic location as possibly
containing a point source.
Training BA consists of building empirical sensor mod-
els based on collected field data (though threats are often
simulated). Distributions of SNR scores are assembled as a
function of exposure on the detector’s surface. Two sensor
models are built: one for the “null” hypothesis (H0) that is
assembled from raw background radiation data and one for
the “alternate” hypothesis (H1) model that is assembled from
data containing injection of a particular source intensity and
type. These empirical models establish a testable expectation
of what new measurements are supposed to look like if they
contain (or do not contain) source signal.
Figures 5(a)-5(b) show example BA sensor models using
the Spectral Anomaly Detector background estimator. Figures
5(c)-5(d) show example BA sensor models using Poisson PCA
as the underlying spectrum SNR estimator.
Given new radiation measurements, BA scores the mea-
surements using the statistical sensor models. BA leverages
the following Bayesian update rule to aggregate probabilities
of data observations Dj∈Dto test a hypothesis H:
(a) Spectral Method Null Model (b) Spectral Method Alternate Model
(c) Poisson PCA Null Hypothesis (d) Poisson PCA Alternate Model
Fig. 5. Example BA sensor models for Spectral Anomaly Detector and
Poisson PCA methods.
P(H|D)∝P(H)Y
Dj∈D
P(Dj|H)(6)
where P(H)is the prior probability (belief) assigned to
hypothesis Hand P(Dj|H)is the empirical data likelihood.
The general strategy is to maintain a set of source hy-
potheses (including possible source parameters such as source
location, intensity, type, etc) about the data. Each hypothesis
is tested for data support using the Bayesian update formula
shown above. For each possible source hypothesis configura-
tion, we test both the alternate hypothesis (H1) that a source
of a particular configuration is present and the null hypothesis
(H0) that a source of the particular configuration is not present
in the data.
Fig. 6. Example BA Test Scenario.
Often times, a rectangular grid is overlaid on the trajectory
to test environment locations as potentially containing the
radiation source. Figure 6 shows an example gridding of a
collected trajectory into a hypothesis space of possible source
locations. To speed up computation, KD-trees help efficiently
find grid points close to the trajectory and trajectory points
close to the gird points. It is assumed that trajectory points far
away from a grid point provide negligible evidence for that
grid point as a source hypothesis.
1) Use of Poisson PCA information in BA: We experi-
mented with the use of Poisson PCA information in the BA
framework. We first built BA sensor models using SNR scores
estimated using Poisson PCA.
As can be seen in Figure 5(d), the SNR trend as a function
of exposure for Poisson PCA for the alternate hypothesis
can differ in shape from the expected SNR trend for a top-
performing Gaussian PCA method like the Spectral Anomaly
Detector (shown in Figure 5(b)). The differences in trend
indicate that Poisson PCA and the Spectral (Gaussian) PCA
may be extracting different information from the same spectra
in flagging spectra as containing source-injection or not.
This conjecture is further supported by a correlation anal-
ysis of Poisson PCA and Spectral Anomaly Detector scores.
TABLE I. SP ECT RA L AND PO ISS ON PCA SNR SC ORE CO RR ELAT ION
COMPARISON
Data Set Spearman Rank Correla-
tion
95% Confidence Intervals
in Rank Correlation
Null Scores 0.1621 [0.1202,0.1862]
Alternate
Scores
0.1410 [0.1018,0.1671]
As can be seen in Table I, Spectral and Poisson PCA scores
are only weakly correlated for both the null and alternate SNR
score distributions. This indicates the methods are detecting
different features of source signals in the same spectra. The
correlation analysis suggested using Poisson PCA and Spec-
tral Anomaly Detector methods in a Combined Aggregation
scheme. The Combined Aggregation method uses a weighted
combination of Poisson PCA and Spectral Anomaly Detector
BA scores after BA is applied to each method.
An experiment was conducted comparing Spectral
Anomaly Detector in BA (“Spectral Aggregation”), and a com-
bined aggregation scheme that used a weighted combination
of Poisson PCA and Spectral Anomaly Detector BA scores
(“Combined Aggregation”).
1,000 bootstrap replicants of a geographic subset of the
data were prepared. Each subset of data was injected with
exactly one radioactive point source using our point source
simulator and a shielded fissile materials source template. The
source count rate was 65 counts/sec at 10m standoff from
the source, while the background count rate was 1263 ±267
counts/sec. A 2m grid of hypothetical source locations was
overlaid on the trajectory and both methods scored each grid
point as possibly being the source location. The region was
scored by both methods with and without source injection.
Fig. 7. Detection results for using Poisson PCA information in BA.
Figure 7 shows the detection accuracy for these methods
with respect to the scores of the top 30 false positives. As
can be seen, the Combined Aggregation method that used
information from both Poisson PCA and Spectral Anomaly
Detector (“Combined Aggregation”) outperformed the method
that just used information from the Spectral Anomaly Detector
in BA (“Spectral Aggregation”). The optimal weights for
the Combined Aggregation were [0.85,0.15] on Spectral and
Poisson PCA scores, respectively. The result suggests that
using Poisson PCA information in BA can help improve threat
detection capability.
2) Incorporation of ZIP Regression Match Filter into BA:
We performed a similar experiment benchmarking the ZIP
Regression Match Filter in BA against other match filters in
BA. We compared the Linear (Gaussian) Regression and ZIP
Regression match filters both on their own and in the BA
framework. We also experimented with marginalizing over the
posterior scores of all of these methods in a combined scheme
(BA-Marg).
1,000 simulated worlds were prepared, each with an in-
jected shielded fissile material point source. The background
had an average count rate of 22 counts/sec with the source
count rate being fewer than 10 counts/sec at 10m standoff. A
2m grid was overlaid onto the world, and all methods scored
the grid points as being the likely location of the source.
Figure 8 shows the Receiver Operating Characteristic
(ROC) detection results of the methods that indicate true
positive rate as a function of the false positive rate.
Fig. 8. Detection results for using ZIP Regression Match Filter information
in BA.
The ZIP Regression Match Filter BA outperforms the Lin-
ear (Gaussian) Regression Match Filter BA. BA-Marg provides
a slight advantage and is technically the method of choice. The
results indicate that using ZIP Regression information in BA
can lead to a more powerful match filter method than simply
using the Linear (Gaussian) Regression Match Filter when the
photon counts in spectra are low.
IV. CONCLUSION
Our study experimented with augmenting the Bayesian
Aggregation (BA) framework with Poisson-based background
estimators to aid analysis of gamma-ray radiation spectra
where the photon count rates of either or both the source and
background are relatively low.
Typically, Gaussian assumptions suffice for estimating the
background and source components of a radiation spectrum
to calculate its SNR when the spectrum contains a sufficient
number of photon counts in its additive components. When the
photon counts in the spectrum from either the background or
source are relatively low, however, the Gaussian approximation
to the Poisson distribution is not effective. In these cases,
background estimators such as the Poisson PCA anomaly
detector or ZIP Regression match filter may be useful in
improving source detection capabilities of radiation threat
detection systems.
The results of our experiments suggest that the use of
Poisson models in background estimation can help improve
threat detection when photon counts from the source (and also
potentially from the background) can be relatively low. Our
study illustrated the use of such Poisson models for a variety
of real world scenarios where this may occur. For instance,
we showed Poisson PCA can help detect a radioactive source
that is faint or far away or when a sensor moves fast by
it. ZIP Regression can help detect a source when smaller,
less sensitive sensors are used for data collection. In all of
these tested cases, the Poisson-based background estimators
appear to improve detection capability. Exploiting the spatial
correlation between measurements in BA can further improve
performance for these challenging source finding problems.
We hope that our results will enable more sensitive and
accurate threat detection as well as possibly provide new
functionalities at the absolute boundaries of detectability with
spectrometers. For example, if mobile radiation detectors need
fewer photon counts to locate a radioactive source, they may
be able to move faster, monitoring wider areas in the same
interval of time. Similarly, if sources can be detected at fainter
SNRs and at larger standoff, there would be substantial impact
on the sensitivity of threat detection systems. The net result is
increasing the safety of the population at risk.
ACKNOWLEDGMENT
This work has been partially supported by the U.S.
Department of Homeland Security, Domestic Nuclear De-
tection Office under competitively awarded grant 2014-DN-
0770ARU087-01, by the U.S. Department of Energy under
grant DE-NA0001736 and by the National Science Foundation
under award 1320347. Lawrence Livermore National Labo-
ratory is operated by Lawrence Livermore National Security,
LLC, for the U.S. Department of Energy, National Nuclear
Security Administration under Contract DE-AC52-07NA27344
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