# Radioactive Source Localisation via Projective Linear Reconstruction

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## Abstract

**:**

## 1. Introduction

#### 1.1. The Nuclear Waste Problem

#### 1.2. Radiation Mapping

#### 1.3. Radioactive Source Localisation

#### 1.4. Micro-Gamma Spectrometry

#### 1.5. Collimation

#### 1.6. Resolving the Issue of Radioactive Source Localisation

## 2. Method

^{3}voxels.

#### 2.1. Fitting the Detector Response Function

#### 2.2. Kaczmarz Deconvolution Optimisation

#### 2.3. Experimental Scenarios

## 3. Results and Discussion

#### 3.1. Scenario 1—Two Sources

#### 3.2. Scenario 2—Four Lower Activity Sources

#### 3.3. Scenario 3—Proximity Limit

#### 3.4. Scenario 4—Mixed Source Strengths

#### 3.5. Quantitative Improvement Measure

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PLR | Projective Linear Reconstruction |

UAV | Unmanned Aerial Vehicle |

DRF | Detector Response Function |

## Appendix A

**Figure A4.**A schematic diagram showing the physical locations of the sources used for scenario 4. The NORM sources are shown in orange and the Cs-137 in green.

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**Figure 1.**Photograph of the KUKA KR 150 system used, with a set of four sealed sources arranged on a table top. Inset—a detailed schematic of the detector and collimator setup.

**Figure 2.**Quadrant cross-section of the as measured Detector Response Function (

**left**) and the fitted model Detector Response Function (

**right**). On the left-hand image, a model detector crystal (collimator and aluminium case not shown) is superimposed to highlight the experimental method. The detector crystal is outlined as an oblong shape with finite volume, although the algorithm assumed a perfect point, and all distances and angles are measured relative to the centre of the crystal.

**Figure 3.**The results from scenario 1—Two similar sources. After processing with (

**a**) simple interpolation, and (

**b**) the PLR algorithm. The scan used a 1 cm resolution. The dashed white circles represent the true location of the source pucks.

**Figure 4.**The results from scenario 2—Four lower activity sources. After processing with (

**a**) simple interpolation, and (

**b**) the PLR algorithm. The scan used a 2 cm resolution. The dashed white circles represent the true location of the source pucks.

**Figure 5.**The results from scenario 3—Proximity limit. After processing with (

**a**) simple interpolation, and (

**b**) the PLR algorithm. The scan used a 1 cm resolution. The dashed white circles represent the true location of the source pucks.

**Figure 6.**The results from scenario 4—Mixed source strengths. After processing with (

**a**) simple interpolation, and (

**b**) the PLR algorithm. The scan used a 1 cm resolution. The dashed white circles represent the true location of the source pucks.

**Figure 7.**(

**a**) Scenario 1 and (

**b**) Scenario 2. Comparison of 1D transects through the interpolated raw measurements (Raw Data) against the best solution estimated by the linear reconstruction technique (PLR data). Best fit Gaussian distributions have been fitted to both to enable a quantitative resolution assessment to be made.

**Table 1.**Current, future arisings and lifetime total expected volumes of different nuclear waste categories. All values are a direct reproduction from the Nuclear Decommissioning Authority report [3]. * This negative value reflects the future conditioning of waste volumes.

Volume (m${}^{3}$) | |||
---|---|---|---|

Waste Category | Reported (as of 1 April 2019) | Estimated Future Arisings | Lifetime Total |

HLW (>10 GBq/kg) | 2150 | −760 * | 1390 |

ILW(<10 GBq/kg) | 102,000 | 145,000 | 247,000 |

LLW (<12 MBq/kg) | 27,400 | 1,450,000 | 1,480,000 |

VLLW (<100 kBq/kg) | 1040 | 2,830,000 | 2,830,000 |

Total | 133,000 | 4,420,000 | 4,560,000 |

Type | Activity (kBq) | X Pos. (cm) | Y Pos. (cm) | |
---|---|---|---|---|

Scenario 1 | Cs-137 | 31.0 | 15.0 | 14.0 |

Cs-137 | 36.0 | 45.0 | 14.0 | |

Scenario 2 | NORM | 2.9 | 13.0 | 12.5 |

NORM | 4.7 | 41.0 | 14.0 | |

NORM | 2.7 | 71.0 | 14.0 | |

NORM | 3.0 | 97.0 | 14.5 | |

Scenario 3 | Cs-137 | 36.0 | 23.5 | 10.0 |

Cs-137 | 31.0 | 35.5 | 10.0 | |

Scenario 4 | NORM | 6.11 | 71.5 | 44.0 |

NORM | 1.38 | 58.0 | 20.5 | |

Cs-137 | 31.0 | 38.9 | 19.7 | |

Cs-137 | 36.0 | 49.5 | 34.0 | |

NORM | 1.21 | 43.5 | 48.0 | |

NORM | 3.49 | 25.5 | 35.3 | |

NORM | 0.97 | 17.8 | 19.7 |

**Table 3.**The standard deviations of the fitted Gaussians as in Figure 7.

Source Number (Left to Right) | Standard Deviation Raw Data (cm) | Standard Deviation PLR Data (cm) | Enhancement | |
---|---|---|---|---|

Scenario 1 | 1 | 7.8 ± 0.2 | 0.78 ± 0.01 | 10 |

2 | 7.6 ± 0.2 | 0.70 ± 0.01 | 10.9 | |

Scenario 2 | 1 | 8.3 ± 0.3 | 0.98 ± 0.01 | 8.5 |

2 | 7.5 ± 0.2 | 1.35 ± 0.01 | 5.6 | |

3 | 8.6 ± 0.3 | 1.37 ± 0.05 | 6.3 | |

4 | 8.0 ± 0.3 | 1.55 ± 0.04 | 5.2 |

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**MDPI and ACS Style**

White, S.R.; Wood, K.T.; Martin, P.G.; Connor, D.T.; Scott, T.B.; Megson-Smith, D.A.
Radioactive Source Localisation via Projective Linear Reconstruction. *Sensors* **2021**, *21*, 807.
https://doi.org/10.3390/s21030807

**AMA Style**

White SR, Wood KT, Martin PG, Connor DT, Scott TB, Megson-Smith DA.
Radioactive Source Localisation via Projective Linear Reconstruction. *Sensors*. 2021; 21(3):807.
https://doi.org/10.3390/s21030807

**Chicago/Turabian Style**

White, Samuel R., Kieran T. Wood, Peter G. Martin, Dean T. Connor, Thomas B. Scott, and David A. Megson-Smith.
2021. "Radioactive Source Localisation via Projective Linear Reconstruction" *Sensors* 21, no. 3: 807.
https://doi.org/10.3390/s21030807