Blind Source Separation of HPGe Output Signals: A New Pulse Pile-up Correction Method

Transcription

1 Adv. Studies Theor. Phys., Vol. 8, 214, no. 16, HIKARI Ltd, Blind Source Separation of HPGe Output Signals: A New Pulse Pile-up Correction Method Abdelhamid Mekaoui 1, El-Mehdi Hamzaoui,2, Rajaa Cherkaoui El Moursli 2 1 LPNR, University Mohammed V Agdal, Faculty of Sciences, Rabat, Morocco 2 National Centre for Nuclear Energy, Sciences and Techniques (CNESTEN), B.P.: 1382 R.P. 11, Rabat, Morocco Copyright 214 Abdelhamid Mekaoui et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The pulse pile-up phenomenon is one of the major problems of the gamma-ray spectrometry, especially at high counting rates. This phenomenon is considered herein, in signal processing point of view, as a blind source separation problem. Indeed, we present in this paper the application of the symetric prewhitening algorithm for the separation of overlapping pulses. The obtained results show that we can achieve the separation task using only three preamplifier's recordings. In case of pulse pile-up, the algorithm allows to separate the stacked pulses into two independent components. A third component is also extracted. This last was found to be strongly correlated to the detector's background noise. Otherwise, the algorithm permits to identify two independent components. Keywords: Blind source separation, gamma-ray spectrometry, Pile-up, SYM-WHITE Corresponding author

2 682 Abdelhamid Mekaoui et al. 1. Introduction Gamma-ray spectrometry is an analytical nuclear technique that is used for the quantitative and qualitative determination of radioisotopes emitting gamma radiation. It is widely applied for the monitoring in nuclear facilities, environment nuclear medicine, and industrial uses of radioisotopes, etc. [1],[2],[3],[4]. Its instrumentation chain is formed by several electronic modules. Typically, an analog spectrometer system can be represented by the block diagram of the following figure 1 [4]. Most gamma spectrometers use a high pure germanium detector (HPGe). Inside it, the interaction photon-matter creates electron-hole pairs which migrate under the effect of a high voltage. This migration generates a current which is measured, amplified and conditioned trough the preamplifier and then digitalized using analog-digital converter. The multichannel analyzer processes the resulting signal and sorts the samples according to high values of energy [1],[2],[3], [4]. Figure 1: Gamma-ray spectrometer block diagram. However, despite technological advances in electronics and computer sciences, this method suffers from several problems related to instrumentation and particle physics. In particular, the stochastic and the noisy nature of the preamplifier's output signal and the pile-up phenomenon are the major problems of this technique. This can make the signals difficult to interpret, induce the distortion of the energy spectrum and, therefore, lead to a loss of information. In order to improve the use of this technique several studies have been conducted to address various issues related to instrumentation. Most of these

3 Blind source separation of HPGe output signals 683 studies, tackle to the use of linear and nonlinear adaptive filtering methods to improve the signal to noise ratio (SNR) at the output of the detector [5],[6],[7]. Others propose some algorithms to correct the pile-up phenomenon [4],[8],[9],[1], [11]. Recently, systems based on digital signal and processors and FPGAs are increasingly introduced to replace the analog systems [3], [12], [13]. In this survey, which represents a continuation of our previous work [14], we are interested in processing and analyzing the signal at the output of an HPGe detector in order to correct the pulse pile-up. This phenomenon occurs when the incidence times of particles are so close that the detector counts them as a single pulse. When this happens, the system can t measure the pulse amplitude correctly, but simply record two or more pulses as a single event with combined intensities by prolonging artificially the Compton continuum [4],[15]. This results in removing the pulses from their proper position in the stripped spectrum, and the area under the full-energy peak will not reflect the correct measure of the total number of full-energy events [4],[15]. We consider here, the pulse pile-up phenomenon as a blind source separation problem and we attempt to isolate each stacked pulse from the recorded preamplifier's output. We demonstrated in [14], that the symmetric prewhitening algorithm is the most effective and suitable method to analyze our sets of data. Consequently, it will be possible, first, to process each extracted independent component individually, then to achieve conditioning and counting of pulses in order to reconstruct the true energy spectrum of the gamma emitter. 2. Materials and Methods 2.1. Signal database We performed three experiments aiming to record the HPGe preamplifier's output signals [16]. In two of them, we exploit a gamma-ray spectrometry chain used for environmental monitoring application whereas in the third, we record the output of an HPGe detector of a neutron activation analysis system. This results in a database formed by 53 recordings, of size of 1 samples each. The signals have been recorded by a high performance digital oscilloscope (Model Tektronix 34) [17] at a sampling frequency of 1MHz. We performed the experiments both in the presence and in the absence of a gamma radiation emitter. This last was composed by a radioactive source of Cesium-137 which allowed us to perform data acquisition at high counting rates SYM-White algorithm As shown in previous works [14], the blind source separation problem of our

4 684 Abdelhamid Mekaoui et al. study case, can be solved using the symmetric prewhitening algorithm (SYM-WHITE). Indeed, according to the values of performance index, this algorithm was found to be the most efficient one among all have the tested methods. Prewhitening can be considered as the basic step in blind source separation task. This signal processing phase performs temporal, spatial or temporal-spatial decorrelation. In particular, it can be used to identify the mixing matrix and perform blind source separation for colored signals [18],[19]. The whitening procedure consists in the transformation a vector x R m into another set y R n through an nxm whitening matrix W [19]. The obtained vectors y, are mutually uncorrelated and have unit variances. In other words, their correlation matrix is an identity matrix: The algorithm SYM-WHITE performs special form of prewhitening procedure. It computes a symmetric prewhitening matrix W on the basis of the covariance matrix R xx, such as: The power of this algorithm is its ability to separate sources under weak conditions and when a mixing matrix is symmetric and the covariance matrix of the original sources is supposed to be identity matrix [18], [19], [2]. 3. Results and discussion In this section, we use the SYM-WHITE algorithm, implemented into the ICALAB-SP TOOLBOX [18], [2], to extract the independent sources. As in [14], we take as mixtures the output of the preamplifier which are recorded in both the presence and absence of radioactive source. As a first step, we determine the number of the mixtures that will constitute the input matrix of the SYM-WHITE algorithm. The optimal dimension corresponds to the best value of the algorithm's performance index [14], [18]. Tests show that only three mixtures allow achieving the best blind separation of the original sources. Also, according to the performance index, we evaluate the best initialization of the mixing matrix W. We found that best results are obtained

5 Blind source separation of HPGe output signals 685 when W is initialized as a Toeplitz matrix [21]. We performed the separation task in both the presence and the absence of the gamma radiation emitter. We found, as the figure 2 below shows, that the analyzed mixtures are formed only by two independent sources. In presence of gamma emitter and when the pile-up phenomenon happens, the algorithm allows separating the pulses and the number of extracted independent sources becomes three (see figure 3). In this case, one of the extracted components is identified to be strongly correlated with the detector's background noise (see figure 4). 2 1st Independent Component nd Independent Component (a) -13 1st Independent Component nd Independent Component (b) Figure 2: Extracted independent components in the presence (a) and absence (b) of gamma radiation emitter.

6 686 Abdelhamid Mekaoui et al. 1st Observation 1st Independent Component nd observation 3rd Observation nd Independent Component rd Independent Component -5 Figure 3: Extracted independent components in case of pulse pile-up. Left: recorded observations. Right: extracted independent components. 1 Normalized cross correlation between 2nd independent component and the detector's background noise Figure 4: Normalized cross-correlation function between the 3 rd extracted component and the detector's background noise in case of pulse pile-up.. 4. Conclusion We use the symmetric prewhitening algorithm to extract independent component from an HPGe preamplifiers' output signals. Indeed, this algorithm, which was found to be the most effective and suitable method to analyze our sets of data, allows us to isolate each pulse even when the pile-up phenomenon happens. The performed tests, both in the absence and the presence of a high energy gamma radiation source, showed that we can perform the separation task

7 Blind source separation of HPGe output signals 687 using only three recordings and when the mixing matrix W is set initially as a Toeplitz one. In this way, the preamplifier's output signals are composed by only two well separated components. However, when the pile-up phenomenon happens, other independent components are extracted. They correspond to the number of pulses that are stacking and forming the pile-up phenomenon. Given the robustness of the blind source separation methods, without a priori assumptions about the relationship that can exist between the various components of analysed mixtures, we propose, in a forthcoming works, to test these signal processing techniques to solve the gamma-neutron separation problem inside nuclear reactors. References [1] International Atomic Energy Agency (IAEA). Guidelines for radioelement mapping using gamma ray spectrometry data. IAEA-TECDOC July 23. [2] American National Standards Institute (ANSI). American National Standard for Calibration and Use of Germanium Spectrometers for the Measurement of Gamma-Ray Emission Rates of Radionuclides. ANSI N , [3] N. Reguigui. Gamma Ray Spectrometry: Practical Information. September [4] T. Trigano. Traitement statistique du signal spectrométrique: étude du désempilement de spectre en énergie pour la spectrométrie Gamma. Thèse de Doctorat, École Nationale Supérieure des Télécommunications, Paris, décembre 25. [5] L. El Badri, E. Hamzaoui, K. Laraki, R. Cherkaoui-Elmorsli, "Adaptive filtering of the preamplifier's output signals of a gamma spectrometry chain", Advanced Studies in Theoretical Physics. Vol. 7, no. 5, , 213. [6] L. Elbadri, E-M. Hamzaoui, K. Laraki, R. Cherkaoui-Elmoursli, "Development of Wavelet Based Tools for Improving the γ-ray Spectrometry", proceedings of the 3 rd International Conference on Advancements in Nuclear Instrumentation, Measurement Methods and their Applications (ANIMMA 213), June 23-27, 213, Marseille, France. [7] G.P. Westphal, K. Jostl, P. Schroder, W. Winkelbauer, "Adaptive digital filter for high-rate high-resolution gamma spectrometry," IEEE Trans. Nucl. Sc., vol. 48, p , 21. [8] O.U. Anders, "Experiences with the Ge(Li) detector for high-resolution gamma ray spectrometry and a practical approach to the pulse pile-up problem," Nucl. Inst. Methods. A, Vol. 68, No. 2, p , 1969.

8 688 Abdelhamid Mekaoui et al. [9] S. Pommé, B. Denecke, J-P. Alzetta, "Influence of pile-up rejection on nuclear counting, viewed from the time-domain perspective," Nucl. Instr. Meth. A, Vol. 426, No. 2 3, p , [1] T. Trigano, T. Dautremer, E. Barat, A. Souloumiac, "Pile-up correction algorithms for nuclear spectrometry," Proceedings de IEEE ICASSP, Vol. 4, p , 25. [11] T. Trigano, A. Souloumiac, T. Montagu, F. Roueff, E. Moulines, "Statistical Pile-up Correction Method for HPGe Detectors," Signal Processing, IEEE Transactions on, Vol.55, No.1, p , 27. [12] M. Bolić, V. Drndarević, "Digital gamma-ray spectroscopy based on FPGA technology", Nucl. Instr. Methods A, Vol. 482, No. 3, p , 22. [13] A. Georgiev, W. Gast, "Digital pulse processing in high resolution, high throughput, gamma-ray spectroscopy", IEEE Trans. Nucl. Sc., Vol. 4, No. 4, p [14] A. Mekaoui, E. Hamzaoui, R. Cherkaoui El Moursli, "Application of blind source separation algorithms to the preamplifier s output signals of an HPGe detector used in γ-ray spectrometry", Advanced Studies in Theoretical Physics, Vol. 8, 214, No. 9, p [15] A. A. Mowlavi, M. de Denaro, M. R. Fornasier, "Monte Carlo Simulation of Pile-up Effect in Gamma Spectroscopy", chapter 7 in "Applications of Monte Carlo Method in Science and Engineering", Ed. InTech, 211. [16] Canberra. Germanium Well Detector C39793 Datasheet. [17] Tektronix Inc. TDS 34A, TDS 36 and TDS 38 Digital Real-Time Oscilloscopes User Manual. [18] A. Cichocki, S. Amari. Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. John Wiley & Sons, 25. [19] A. Cichocki, S. Osowski, K. Siwek, Prewhitening Algorithms of Signals in the Presence of White Noise, 6 th International Workshop Computational Problems of Electrical Engineering, September 1-4, 24, Zakopane, Poland, p.p [2] A. Cichocki, S. Amari, K. Siwek, T. Tanaka, Anh Huy Phan et al., ICALAB Toolboxes, Version 3., [21] A. Böttcher, S.M. Grudsky, "Toeplitz matrices, asymptotic linear algebra, and functional analysis". Springer. 2. Received: May 15, 214