1. Muon Tomography Algorithms for Nuclear Threat Detection
R. Hoch, D. Mitra, M. Hohlmann, K. Gnanvo

2. Tomography Imaging by sections Used in many applications
Image different sides of a volume
Use reconstruction algorithms to combine 2D images into 3D
Used in many applications
Medical
Biological
Oceanography
Cargo Inspections?

3. Muons Cosmic Ray Muons More massive cousin of electron
Produced by cosmic ray decay
Sea level rate 1 per cm^2/min
Highly penetrating, but affected by Coulomb force

4. Muon Tomography
Previous work imaged large structures using radiography
Not enough muon loss to image smaller containers
Use multiple coulomb scattering as main criteria

5. Muon Tomography Concept

6. Reconstruction Algorithms
Point of Closest Approach (POCA)
Geometry based
Estimate where muon scattered
Expectation Maximization (EM)
Developed at Los Alamos National Laboratory
More physics based
Uses more information than POCA
Estimate what type of material is in a given sub-volume

7. Simulations Geant4 - simulates the passage of particles through matter
CRY – generates cosmic ray shower distributions

8. POCA Concept
Incoming ray 3D
POCA
Emerging ray

9. 40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
POCA Result
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
Unit: mm
Θ (degrees) U W Z Pb Fe Al X Y

10. POCA Discussion Pro’s Con’s Fast and efficient
Can be updated continuously
Accurate for simple scenario’s
Con’s
Doesn’t use all available information
Unscattered tracks are useless
Performance decreases for complex scenarios

11. Expectation Maximization
Explained in 1977 paper by Dempster, Laird and Rubin
Finds maximum likelihood estimates of parameters in probabilistic models using “hidden” data
Iteratively alternates between an Expectation (E) and Maximization (M) steps
E-Step computes an expectation of the log likelihood with respect to the current estimate of the distribution for the “hidden” data
M-Step computes the parameters which maximize the expected log likelihood found on the E step

12. Basic Physics Scattering Angle Scattering function
Distribution ~ Gaussian Non-deterministic (Rossi)

13. EM Concept L T
Voxels following
POCA track

14. Algorithm gather data: (ΔΘx, Δθy, Δx, Δy, pr^2)
estimate LT for all muon-tracks
initialize λ (small non-zero number)
for each iteration k=1 to I
for each muon-track i=1 to M
Compute Cij - E-Step
for each voxel j=1 to N
M-Step
return λ

15. Scenario 1 Geometry
5 40cmx40xcmx20cm Boxes

16. 10 minutes exposure 10cmx10cmx10cm voxels
Scenario 1 Results
10 minutes exposure
10cmx10cmx10cm voxels
Axis in mm
Λ (mrad^2/cm) Z X Y

17. Scenario 1 Results Accuracy Test 48000 total voxels, 32 Uranium
Threshhold: 1000
True Positives: 25
False Negatives: 7
True Positive Rate: 78.1%
False Positives: 119
False Positive Rate: %

18. Simulated Truck Red Boxes are Uranium Blue are Lower Z Materials
Scenario 2 Geometry
Simulated Truck
Red Boxes are Uranium
Blue are Lower Z Materials

19. 10 minutes exposure 5cmx5cmx5cm voxels
Scenario 2 Results
10 minutes exposure
5cmx5cmx5cm voxels
Axis in mm
Λ (mrad^2/cm) Z X Y

20. Scenario 2 Results Accuracy Test 9704448 total voxels, 106 Uranium
Threshhold: 1000
True Positives: 90
False Negatives: 16
True Positive Rate: 85%
False Positives: 62
False Positive Rate: %

21. Median Method
Rare large scattering events cause the average correction value to be too big
Instead, use median as opposed to average
Significant computational and storage issues
Use binning to get an approximate median

22. Aproximate Median Cij = -357,000 Cij = -45,000 Cij = 25,000
Bin Size = 100,000 5 10 20 18 9 11 15 21 23 7
-400,000-
-300,000
-200,000
-100,000
100,000
200,000
300,000
400,000+ 5 15 35 53 62 73 88
109
132
139
Total Tracks = 139
Median Track at 70
Track 70 in Bin 6
Take Average of Bin 6 (Total Value of Cij's / 11)

23. Scenario 1 Results 10 minutes exposure 5cmx5cmx5cm voxels Axis in mm
Λ (mrad^2/cm) Z X Y

24. Scenario 1 Results Accuracy Test 48000 total voxels, 32 Uranium
Threshhold: 500
True Positives: 26
False Negatives: 6
True Positive Rate: 81.1%
False Positives: 31
False Positive Rate: %

25. Scenario 2 Results 10 minutes exposure 5cmx5cmx5cm voxels Axis in mm
Λ (mrad^2/cm) Z X Y

26. Scenario 2 Results Accuracy Test 9704448 total voxels, 106 Uranium
Threshhold: 500
True Positives: 97
False Negatives: 9
True Positive Rate: 91.5%
False Positives: 5
False Positive Rate: %

27. Future Work Improvement of absolute lambda values Real-time EM
Analysis of complex scenarios

28. Thanks!

29. Timing Scenario 1: Average Method: 316s
Approximate Median Method: 1533s
Median Method: ~12hrs
Scenario 2:
Average Method: 1573s
Approximate Median Method: 7953s
Median Method: +30hrs

30. Why Muon Tomography? Other ways to detect: Muon Tomography advantages:
Gamma ray detectors (passive and active)
X-Rays
Manual search
Muon Tomography advantages:
Natural source of radiation
Less expensive and less dangerous
Decreased chance of human error
More probing i.e. tougher to shield against
Can detect non-radioactive materials
Potentially quicker searches