1. Simulation Study of Muon Scattering For Tomography Reconstruction
Presented at
NSS-MIC 2009 Orlando
Florida Institute of Technology
K. Gnanvo
M. Hohlmann
D. Mitra
A. Banerjee
4/25/2017
Decision Sciences, San Diego, April 2010

2. Decision Sciences, San Diego, April 2010
Muon Scattering
Scattering angle Scattering function
distribution: Approx. Normal (Bethe 1953)
Heavy tail over Gaussian
milirad 2 /cm
4/25/2017
Decision Sciences, San Diego, April 2010

3. Decision Sciences, San Diego, April 2010
Types of Tomography
Emission tomography:
SPECT
PET
MRI
Transmission tomography
X-ray
Some Optical
Reflection
UltraSound
Total Internal Reflection Fluoroscopy (TIRF)
Scattering/ Diffusion
Muon tomography
Some Optical (IR) tomography
4/25/2017
Decision Sciences, San Diego, April 2010

4. Decision Sciences, San Diego, April 2010
Experiment
GEANT4 simulation with partial physics for
scattering
Large array of Gas Electron Multiplier (GEM)
detector is being built
IEEE NSS-MIC’09 Orlando Poster# N13-246
4/25/2017
Decision Sciences, San Diego, April 2010

5. Reconstruction Algorithms
Point of Closest Approach (POCA)
Purely geometry based
Estimates where each muon is scattered
Max-Likelihood Expectation Maximization for Muon Tomography
Introduced by Schultz et al. (at LANL)
More physics based-model than POCA
Estimates Scattering density (λ) per voxel
4/25/2017
Decision Sciences, San Diego, April 2010

6. Decision Sciences, San Diego, April 2010
POCA Concept
Incoming ray 3D
POCA
Emerging ray
Three detector-array above and three below
4/25/2017
Decision Sciences, San Diego, April 2010

7. POCA Result ≡ processed-Sinogram?
40cmx40cmx20cm Blocks (Al, Fe, Pb, W, U)
Unit: mm Θ U W Pb Fe Al
4/25/2017
Decision Sciences, San Diego, April 2010

8. Decision Sciences, San Diego, April 2010
POCA
Pro’s
Fast and efficient
Accurate for simple scenario’s
Con’s
No Physics: multi- scattering ignored
Deterministic
Unscattered tracks are not used
4/25/2017
Decision Sciences, San Diego, April 2010

9. Decision Sciences, San Diego, April 2010
ML-EM System Matrix L T
Voxels following
POCA track
Dynamically built for each data set
4/25/2017
Decision Sciences, San Diego, April 2010

10. ML-EM Algorithm // Mj is # tracks
(adapted from Schultz et al., TNS 2007, & Tech Reports LANL)
gather data: (ΔΘ, Δ, p): scattering angles, linear displacements, momentum values
estimate track-parameters (L, T) for all muons
initialize λ (arbitrary small non-zero number, or…)
for each iteration k=1 to I (or, until λ stabilizes)
for each muon-track i=1 to M
Compute Cij
(2) for each voxel j=1 to N
// Mj is # tracks
(5) return λ
4/25/2017
Decision Sciences, San Diego, April 2010

11. Decision Sciences, San Diego, April 2010
ML-EM Reconstruction
[In ‘Next Generation Applied Intelligence’ (Springer Lecture Series in Computational
Intelligence: 214), pp , June 2009.]
Slow for complex scenario
Our implementation used some smart
data structure for speed and better
memory usage
4/25/2017
Decision Sciences, San Diego, April 2010

12. POCA Result for a vertical clutter
4/25/2017
Decision Sciences, San Diego, April 2010

13. Decision Sciences, San Diego, April 2010
Slabbing Concept
Slabbing Slice
3cm thick
4/25/2017
Decision Sciences, San Diego, April 2010

14. Decision Sciences, San Diego, April 2010
“Slabbing” studies with POCA: Filtered tracks with DOCA (distance of closest approach) Ev: 10Mil Vertical stack: Al-Fe-W: 50cm50cm20cm, Vert. Sep: 10cm Slab size: 3 cm
4/25/2017
Decision Sciences, San Diego, April 2010

15. POClust Algorithm: clustering POCA points
Input: Geant4 output (list of all muon tracks and associated parameters)
1. For each Muon track {
2. Calculate the POCA pt P and its scattering-angle
if (P lies outside container) continue;
4. Normalize the scattering angle (angle*p/3GeV).
5. C = Find-nearest-cluster-to-the (POCA pt P);
Update-cluster C for the new pt P;
After a pre-fixed number of tracks remove sporadic-clusters;
Merge close clusters with each-other }
9. Update λ (scattering density) of each cluster C using straight tracks passing through C
Output: A volume of interest (VOI)
4/25/2017
Decision Sciences, San Diego, April 2010

16. Decision Sciences, San Diego, April 2010
POClust essentials
Not voxelized, uses raw POCA points
Three types of parameters:
Scattering angle of POCA point
Normalized “proximity” of the point to a cluster
how the “quality” of a cluster is affected by the new poca point and
merger of points or clusters
Real time algorithm: as data comes in
4/25/2017
Decision Sciences, San Diego, April 2010

17. Decision Sciences, San Diego, April 2010
POClust Results
Medium: Air
G4 Phantom
U,W,Pb,Fe,Al
Size: 40X40X20cm
4/25/2017
Decision Sciences, San Diego, April 2010

18. Three target vertical clutter scenarioFe W Al Fe
Al-Fe-W: 40cm*40cm*20cm 100cm gap W
4/25/2017
Decision Sciences, San Diego, April 2010

19. Three target vertical clutter scenario: Smaller gap
Al-Fe-W: 40cm*40cm*20cm
10cm gap Al Fe W
4/25/2017
Decision Sciences, San Diego, April 2010

20. POClust Results: Reverse Vertical Clutter
Medium: Vacuum U Pb Al
U-Pb-Al
Size:40X40X20cm
Gap:10cm
4/25/2017
Decision Sciences, San Diego, April 2010

21. Decision Sciences, San Diego, April 2010
POClust Results
Medium: Vacuum
U inside Pb box
U size: 10X10X10cm
Pb Box: 200X200X200 cm
Thickness(Pb box): 10cm
4/25/2017
Decision Sciences, San Diego, April 2010

22. Why POClust & Not just POCA visualization?
Quantitate: ROC Analyses
Improve other Reconstruction algorithms
with a Volume of Interest (VOI) or
Regions of Interest (ROI)
Why any reconstruction at all?
POCA visualization is very noisy in a
complex realistic scenario
4/25/2017
Decision Sciences, San Diego, April 2010

23. Additional works with POClust
Clustering provides Volumes of Interest (VOI) inside the container: Run ML-EM over only VOI for better precision and efficiency
Slabbing, followed by Clustering
Clusters growing over variable-sized hierarchical voxel tree, followed by ML-EM
Automated cluster-parameter
selection by optimization
5. Use cluster λ values in a Maximum
A Posteriori –EM, as priors (Wang
& Qi: N07-6)
4/25/2017
Decision Sciences, San Diego, April 2010

24. POClust as a pre-processor
Volume of Interest reduces after Clustering:
A minimum bounding box
(235cm X 235cm X 45cm)
Initial Volume of Interest (400cm X 400cm X 300cm)
4/25/2017
Decision Sciences, San Diego, April 2010

25. EM after pre-processing with POClust
Scenario: 5 targets
VOI : 400X400X300 cm3
Iterations: 50
Targets:
Uranium (100,100,0),
Tangsten (-100, 100, 0) W U
4/25/2017

26. Results From EM over POClust generated VOI
Scenario: U, W, Pb, Al, Fe placed horizontally
Important Points:
IGNORE ALL VOXELS OUTSIDE ROI
EM COMPUTATION DONE ONLY INSIDE ROI
After Clustering, VOI reduces,
#Voxels = 18330
Here, Total Volume = 400 X 400 X 300 cm
Voxel Size= 5 X 5 X 5 cm
#Voxels =
Iterations
Actual Volume
(400 X 400 X 300 cm)
Time taken (seconds)
Clustered Volume
(235 X 235 X 45 cm )
100
113.5
21.5 60
99.54
20.2 50
95.6
19.5 30
84.48
17.4 10
79.27
16.0
4/25/2017

27. A human in muon! …not on moon, again, yet …
Twenty million tracks
In air background
130cmx10cmx10cm Ca slab inside
150cmx30cmx30cm H2O slab
GEANT4 Phantom
4/25/2017
Decision Sciences, San Diego, April 2010

28. Department of Homeland Security National Science Foundation
Thanks!
Acknowledgement:
Department of Homeland Security
National Science Foundation
& many students at FIT
Debasis Mitra
4/25/2017
Decision Sciences, San Diego, April 2010