Abstract
This chapter presents some recent data processing developments associated with radiation monitoring systems. Radiation monitors have to continuously provide count rate estimations with accuracy and precision. A filtering technique based on a Centered Significance Test coupled with a Brown’s double exponential filter has been developed and used in compensation measurement and moving sources detection schemes.
Keywords
- data processing
- nuclear counting
- radiation monitor
- signal processing
- filtering
- frequentist inference
1. Introduction
During the last decades, ionizing ray detectors have grown in performance, thanks to digital electronics developments (ADC and FPGA), allowing for an advanced processing of nuclear impulse signals. It is also noteworthy that this field has favored the development of real-time processing algorithms dealing with count rate data.
The architecture of a typical nuclear measurement system is presented in Figure 1. It can be divided in four parts:
Voltage supply,
Detector part,
Front-end electronics,
User interface.
The detector part contains the physical sensor (noble gas, scintillation material, and semiconductor) in which radiation interacts with matter. A conversion unit (preamplifier or photo-converter) converts the induced charges or photons in amplified voltage pulses. In the case of gas or semiconductor-based sensors, a high voltage is required to polarize the medium, and a low voltage is needed to supply active components of the preamplifier. In the case of scintillators, a high voltage supplies the photomultiplier.
Front-end electronics is composed of an analog filter, an analog-to-digital converter (ADC), and a digital filter. An analog shaping filter can be used to adapt the signal before digital conversion (dynamic range and respect to Shannon rules), and/or to maximize signal-to-noise ratio (SNR). The ADC digitalizes the signal with a given frequency and resolution.1 This digital signal is processed into a fast electronic component, typically a microcontroller, or a field-programmable gate array (FPGA). The embedded firmware has to comply with the very high-frequency of the ADC output with a processing period in the range of 1–10 ns. The algorithms implemented in the firmware perform the pulse processing, which mainly consists in triggering, first digital filtering for SNR maximization, stabilizing the baseline, estimating the dead time, and counting a number of pulse events
An interface is built on a computer connected with the front-end electronic card. The software reads, at each given time interval ∆
This chapter will not address pulse processing techniques, for which details can be found in [1–3], but presents some recently developed techniques to process count rate signal using frequentist inference. Bayesian inference can also be implemented to process count rate as for instance for gamma spectrum unfolding or photon-limited imaging filtering [4, 5]. These are very efficient to accurately processed nuclear counting data, but become unsuited of online applications. After describing the theoretical model of the counting process, a smoothing technique will be presented as a fundamental building block, ensuring an online and adaptive filtering of the signal. The issue of composite measurements will then be addressed with a method allowing improving metrological reliability for particle discrimination (compensation technique). Finally, the use of detectors in a network to address moving source detection will be developed.
2. Nuclear counting model
Nuclear disintegration can occur following different processes depending on the
Subsequently, the daughter nucleus is, most of the time, released in an exited state and usually reaches its fundamental level by gamma-ray emission:
According to the detector type,
The observation of an unstable nucleus over a time
The probability
In a radioactive source containing a population of
In practice,
Expectation and variance of the number of decays are equal to
At each time
A challenge in radiation monitoring is to provide count rate estimation
3. Count rate smoothing
The aim of smoothing algorithms is to improve the estimation of
where
The relative stochastic uncertainty
In practice, counting processes are not homogenous (
First approaches consist in the implementation of preset count filter providing a fixed variance
Among FIR filters, the exponential moving average (EMA) remains widespread [7, 8], but do not fully deals with the tread-off issue between accuracy and precision.
The algorithm translation of the actualization of
In a first approach [10], a sequential probability ratio test (SPRT) has been assessed under the assumption that
In the rest of the discussion, we will conventionally use notation
In the CST test, the vector
The method is based on a comparison between actual and expected distributions of
The expectation
We will note
Under
In practice, for embedded implementations, it is impossible to sample and interpolate distributions
where Φ is the cumulative distribution function of the centered Normal law.
As illustrated in Figure 4,
If
Under
As illustrated in Figure 4,
An equivalent confidence level 1 −
With
When
If
The number
If
At every elementary time step ∆
With
This nonlinear approach performs advantageously in comparison with conventional linear filters [12, 14], allowing to maintain sufficient precision while rate changes in the signal occur.
Remaining high-frequency fluctuations can now be reduced using a second, recursive smoother, for instance a Brown’s double exponential filter [14]. A first exponential smoothing
With
A last exponential smoothing
With
The parameter
Finally, the Brown’s estimation
With
Figures 5 and 6 illustrate the advantage of the hereby described nonlinear filters over conventional, moving average filters with a 20% rate variation, respectively, in a low count rate configuration (5 counts per sample) and in a higher count rate configuration (500 counts per sample). The nonlinear filter has been set with parameters
Such nonlinear smoothing algorithms, easily embedded into programmable components, have for instance been implemented into a Geiger-Müller dosimeter fixed on a wireless robot used for radiological threat detection [15]. This algorithmic building block is plays a key role in the nuclear counting methods studied in the next sections, namely compensation measurements and sensor network processing.
4. Compensation measurement
In many cases, radiation monitoring requires the counting of a signal from a first radiation source within an interference signal induced by a second particle emitter, namely α/β vs. γ;
where
increase in fluctuation level;
apparition of negative count rates without physical sense;
loss of reliability (impact of energy and anisotropy of the background signal).
Values of
The expectation and the variance of the random variable
Reduced variances
If the compensation factor
In practice, the factor
The estimation of
Based on the generalized variance expressed in Eq. (43), a hypothesis test is built to select positive and significant values of
Algorithm 1:
If
Then
Else
Figure 7 synthetizes the principle, inputs, and outputs of the compensation technique.
The method improves the reliability of compensation measurement with the use of a recorded database. Moreover, accuracy and decision threshold
As a perspective, it has been demonstrated that the multiplication of channels, such as illustrated in Figure 8, allows the system to learn a prior distribution for the signal over a set of pixels as a function of incident energy and spatial origin of background particles. Dispatching
5. Moving source detection
Radiation portal monitors (RPM) are implemented to detect radioactive sources, carried by a vehicle in motion, through the monitoring of a count rate measured by large-volume detectors. Two main issues arise in RPM development: correcting the shadow shielding effect observed when the vehicle is dense enough to impact the baseline of the signal, and improving the detection capability (increasing true detection minus false alarm detection probability).
RPM detection strategy is based on a hypothesis test where the estimated signal
During the passage of a dense vehicle,
If
This effect, so-called “shadow effect,” induces a significant loss in detection capability (
Many works have been done in order to restore the baseline (
In the first place, the minimization of
Estimations are continuously recorded into an historical memory with a depth
with
The trend of the signal, which can be constant, decreasing or increasing, is represented by a slope state
with
The state of the signal
States
Knowing the state of the system, the baseline of the signal can be restored. The upper level (
The baseline is restored to obtain corrected count rate estimations
∀
Figure 11 illustrates the baseline restoration: the correction algorithm enables the detection of a source originally hidden by shadow effect. A simulation study has shown the significant gain in detection probability with the maintaining of a stable false detection rate [24].
The conception of a RPM primarily consists in designing detection blocks with a maximized sensitivity according to the application view and cost-effectiveness strategies. Signal processing is then to be implemented in the system in order to tune its detection capabilities. The improvement of RPM performance forms an active topic of research. It has notably been established that the spectral analysis of the signal, even for unresolved detectors, allows a gain in detection performance [25]. Another upgrade can be achieved by time series analysis techniques, especially when RPM are deployed in a network, which allows the implementation of correlation methods [26]. Figure 12 presents the schematic of a RPM network implementing
The network configuration enables two complementary types of detection: the first one based on traditional temporal analysis of individual channel
A correlation vector
For the vehicle passing from detectors 1 to
The algorithm firstly determines a phase
The detection test reads:
Algorithm 2:
If
Then
Else
The use of the empirical variance
with
The detection algorithm mixes the detection according to each individual channel with the detection using the correlation factor. In both cases, a decision threshold (
And let
Algorithm 2 presents the mechanism of the cumulative detection.
Algorithm 3:
If
And if
Then, the detection hypothesis H0 is accepted and the hypothesis H1 is rejected,
Else if
Then, the detection hypothesis H1 is accepted and the hypothesis H0 is rejected,
Or if
Then, the detection hypothesis H1 is accepted and the hypothesis H0 is rejected,
And, the velocity of the source is equal to
It has been proven in [27–29], the largely significant added-value in term of detection capability permits by the implementation of the correlation based detection. The true detection rate is increased while maintaining very low false alarm rate. Figure 13 presents a system realized by the CEA which implements the correlation method [30].
All of these algorithms will be implemented in a dedicated DSP card [3] and the compliance of the RPM system will the standard ANSI42-35 will be tested in due course [31].
6. Conclusion
Different count rate processing methods have been presented in this chapter: an adaptive smoother, a background discrimination method and two algorithms improving the detection of moving sources. In these algorithms, frequentist inferences are realized on the basis of measured data. These types of approaches are well suited for real-time processing, allowing taking decision with very few iterations, compared to Bayesian inferences which are more suited for post-processing analyses.
The nonlinear smoother is proved to be a key building block in radiation monitors, delivering a fine estimation of count rate expectation with a minimized associated variance. Both expectation and variance estimations are used to apply hypothesis tests addressing many problematics in radiation monitoring such as for instance those already developed hereby: compensation and RPM network.
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Notes
- Current ADCs are available with tradeoffs between resolution and sampling frequency such as: 16 bit / 100MS/s and 8 bit / 1 GS/s. CAEN Electronic instrumentation, 724 Digitizer Family, CEAN data sheet, 2015.