Journal of Spectroscopy

Volume 2019, Article ID 8360395, 9 pages

https://doi.org/10.1155/2019/8360395

## Improving Neutron-Gamma Discrimination with Stilbene Organic Scintillation Detector Using Blind Nonnegative Matrix and Tensor Factorization Methods

^{1}ESMAR Laboratory, Mohammed V University in Rabat, Faculty of Sciences, Rabat, Morocco^{2}National Centre for Nuclear Energy, Science and Technology (CNESTEN), Rabat, Morocco

Correspondence should be addressed to Hanane Arahmane; moc.liamtoh@1ra_enanah

Received 22 November 2018; Revised 14 March 2019; Accepted 18 April 2019; Published 30 May 2019

Academic Editor: Jose S. Camara

Copyright © 2019 Hanane Arahmane 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

In order to perform highly qualified neutron-gamma discrimination in mixed radiation field, we investigate the application of blind source separation methods based on nonnegative matrix and tensor factorization algorithms as new and robust neutron-gamma discrimination software-based approaches. These signal processing tools have allowed to recover original source components from real-world mixture signals which have been recorded at the output of the stilbene scintillation detector. The computation of the performance index of separability of each tested nonnegative algorithm has allowed to select Second-Order NMF algorithm and NTF-2 model as the most efficient techniques for discriminating neutrons and gammas. Furthermore, the neutron-gamma discrimination is highlighted through the computation of the cross-correlation function. The performance of the blind source separation methods has been quantified through the obtained results that prove a good neutron-gamma separation.

#### 1. Introduction

Neutron detection has been applied in many diverse fields from the scientific to industrial. The scintillation detectors [1] are the most adopted for neutron detection and preferred means for neutron spectroscopy purposes. However, their sensitivity to gamma-rays disturbs the estimation accuracies of the neutron pulses [1]. Within this framework, various researches have been done using digital and analog techniques to discriminate neutrons from the background gamma-rays. Due to their specific feature of organic scintillation and varying quality of discrimination, pulse shape discrimination (PSD) methods were commonly used to perform the neutron-gamma discrimination [2]. The most popular ones are charge comparison [3], rise time [4], zero-crossing [4] as PSD conventional methods, and pulse gradient analysis (PGA) as PSD digital one [5]. The quality of neutron-gamma discrimination using these standard PSD methods has been quantified by Figure of Merit (FOM) metric. A high FOM value is interpreted as a good discriminator between the pulses generated by neutrons and gamma-rays. Nevertheless, in the presence of pulse pile-up, FOM is not able to well discriminate the gamma contribution and can be a little misleading [6]. Thus, we can say that the PSD methods are insufficient to perform the separation task with high precision.

With the progress of digital pulse processing (DSP) tools and in order to improve the accuracy of neutron-gamma discrimination, novel approach-based on blind source separation has been proposed known as the most popular unsupervised learning techniques. We have used in our previous works, the Nonnegative Matrix Factorization (NMF) methods to analyze fission chamber’s output signals, produced using simulation codes, for neutron flux monitoring purpose [7]. The Nonnegative Tensor Factorization (NTF) algorithms has been applied by Laassiri et al. to recover the original sources from simulated signals recorded by fission chambers in order to achieve the neutron-gamma discrimination task [8].

The main objective of this work is to analyze the output signals of stilbene scintillation detector, through both NMF and NTF techniques, in order to extract the original independent sources, also called Independent Components (ICs). The computation of the performance index of separability (PI) of each NMF and NTF algorithm allows selecting the most efficient one. The extracted sources will be characterized using cross-correlation function as an object function to separate neutrons from gamma-rays background.

This paper is organized as follows. The first part consists of describing the theory of the blind source separation methods (Section 2). Secondly, we briefly present the experimental setup employed to obtain the datasets used in this work (Section 3). Then, we develop our new discrimination approach based on blind source separation techniques (Section 4). At last, the obtained results will be illustrated (Section 5).

#### 2. Blind Nonnegative Matrix and Tensor Factorization Methods

In this work, we tackle the neutron-gamma discrimination problem from a Blind Source Separation (BSS) point of view. In general, the BSS regroups the methods used to solve the problem of recovering mutually independent components, called sources, from a set measured sensor signals (or observations). These last are mixtures formed through an unknown system, during the propagation of the information from its original sources to sensors in addition to the background noise introduced by the sensors themselves.

Indeed, we have decided to use NMF and NTF methods in order to extract the ICs from signals recorded at the output of stilbene scintillation detector. The computation of the PI values of each NMF and NTF algorithms allows selecting the most appropriate one and is suitable to analyze our set of nuclear data. This selection is confirmed through the measure of the signal-to-interference ratio (SIR) that is determined the accuracy of the sources separation. Furthermore, the computation of the cross-correlation function between the extracted ICs and pure neutron and gamma signals allows us to achieve a better characterization of the neutron and gamma-ray signals.

The ability of our proposed methods to recover the original sources from observed mixtures without any requirements on the analyzed mixtures or the mixing process enables us to apply them under any neutron and gamma energy ranges. Moreover, the dimensionality reduction sought in many applications and the nonnegativity constraints allow better-modeled and interpreted neutron and gamma signals with ideally sparse or smooth components.

##### 2.1. Nonnegative Matrix Factorization

The main goal of the NMF is to find lower-rank nonnegative matrices for recovering the sources (or hidden components) with specific structures and physical interpretations. The recovered sources are then characterized through the computation of the cross-correlation function to perform the neutron-gamma discrimination. The high performance of this function for evaluating the degree to which two signals are similar and its computation simplicity are two main reasons behind chosen cross-correlation function to perform the discrimination purpose.

Many researchers, e.g., Paatero and Tapper [9] have investigated the NMF methods, but they have only acquired popularity since the publication of the works of Lee and Seung [10, 11]. They have proposed a simple multiplicative update algorithm to find nonnegative representations of nonnegative signals and images [10]. The nonnegativity constraint is usually presented as the origin of the NMF robustness to provide a perceptual decomposition of the data.

The NMF [12] is an analogous technique of linear algebra for reducing the ranks of matrices with positive value atoms that can be more easily interpretable and semantically more relevant. The NMF approximates *Y* as a product between two matrices null or positive as follows [12]:where(i) is the matrix of observed data, with *M* being mixed signal and *T* being corresponding number of samples,(ii) is a mixing matrix with , with *R* being number of estimated components,(iii) is the matrix of original nonnegative sources with ,(iv) is a noise or error matrix.

The standard approach to NMF is the alternating minimization of a specific cost function [13]. It is presented in the Appendix A of this paper.

##### 2.2. Nonnegative Tensor Factorization

For some applications, the matrices are considered as second-order tensors. Usually, they can go up to the third or higher order. Thus, the NMF can be generalized to the NTF.

The NTF is a technique for decomposing and computing a nonnegative parts-based representation of high-dimensional data (tensor) into sparse and reasonably interpretable components with the constraint of the nonnegativity. It has been successfully applied to numerous data analysis problems in various fields [14, 15]. The multiway data is one of the important methods of the NTF decomposition. From the point of view of data analysis, the NTF is very interesting because it takes into account the spatial and temporal correlations between the variables accurately more precise [16].

The NTF problem is based on a nonnegative canonical decomposition/parallel factor decomposition denoted by CANDECOMP and PARAFAC, respectively, [17] and imposes nonnegative constraints on tensor and factor matrices. The mathematical formalism of NTF is as follows [12, 18].

Given an *N*-th order data tensor and a positive integer *J*, factorize into a set of *N* nonnegative component matrices , representing loading matrices (or factors), that can be expressed as:

With and is the outer product of the tensors.

The tensor is an approximation error and is the identity tensor. Figure 1 illustrates the decomposition for a third-order tensor.