Angle Statistics Reconstruction: a robust reconstruction algorithm for Muon Scattering Tomography

Abstract

Muon Scattering Tomography (MST) is a technique for using the scattering of cosmic ray muons to probe the contents of enclosed volumes. As a muon passes through material it undergoes multiple Coulomb scattering, where the amount of scattering is dependent on the density and atomic number of the material as well as the path length. Hence, MST has been proposed as a means of imaging dense materials, for instance to detect special nuclear material in cargo containers. Algorithms are required to generate an accurate reconstruction of the material density inside the volume from the muon scattering information and some have already been proposed, most notably the Point of Closest Approach (PoCA) and Maximum Likelihood/Expectation Maximisation (MLEM) algorithms. However, whilst PoCA-based algorithms are easy to implement, they perform rather poorly in practice. Conversely, MLEM is a complicated algorithm to implement and computationally intensive and there is currently no published, fast and easily-implementable algorithm that performs well in practice. In this paper, we first provide a detailed analysis of the source of inaccuracy in PoCA-based algorithms. We then motivate an alternative method, based on ideas first laid out by Morris et al, presenting and fully specifying an algorithm that performs well against simulations of realistic scenarios. We argue this new algorithm should be adopted by developers of Muon Scattering Tomography as an alternative to PoCA.

A compact, high resolution tracker for cosmic ray muon scattering tomography using semiconductor sensors

“…Figure 17 shows the effect of smoothing and quantile choice in the x y-projection of a 15 × 25 × 55 mm 3 lead sample imaged using 45000 muons. As discussed in [16], the algorithm performs well over a large range of quantiles, and in this paper a 0.8 quantile and 4 × 4 × 4 mm 3 volume elements are found to give best contrast between the sample and background.…”

“…The Angle Statistics Reconstruction (ASR) algorithm is used for the image reconstruction in this study. ASR is chosen as it is robust to changes in the system setup, easy to implement and has been shown to perform better than Point of Closest Approach (PoCA) algorithms [16]. For a given volume element, the algorithm stores a score for each event that has the shortest distance between the volume element and the incoming and outgoing muon tracks below a threshold distance.…”

“…The fixed fraction is referred to as the 'quantile'. For a detailed description of the algorithm, its motivation and performance see [16].…”

A quantitative assessment of Imaging High-Z and Medium-Z materials using Muon Scattering Tomography

“…The muon trajectories are reconstructed using dedicated algorithms. In this paper, we consider three frequently-used algorithms; the simple Point of Closest Approach (PoCA) algorithm [11] (see section 3.1), the Angle Statistics Reconstruction (ASR) algorithm [12] (see section 3.2), and the Binned Clustering (BC) algorithm [13] (see section 3.3). All these algorithms divide the volume of interest into a 3D cubic-voxel grid with a side length of typically 10 mm for each voxel.…”

Multiparametric approach to the assessment of muon tomographic results for the inspection of a full-scale container

“…Moreover, this method may discard part of the tracks, when the intersection of the incoming and outgoing tracks is located in a voxel which lies outside the volume of interest. This has motivated the implementation of several alternative imaging methods [13,19,[23][24][25][26][27][28][29]. Among others, log-likelihood algorithms, two-point autocorrelation analyses, density-based clustering algorithms and friends-of-friends strategies have been sometimes used, even by ourselves [13,19], since they are based on more realistic physical and statistical assumptions, and allow to tackle the problems encountered with the Poca algorithm.…”